how to solve by completeing the square  7^2 -2x - 2 = 0?
959661
if by this you mean\n\nx^2 - 2x - 2 = 0\n\nx^2 - 2x = 2\nx^2 - 2x + 1 = 3\n(x - 1)^2 = 3\nx - 1 = sqrt(3)\nx = 1 ± sqrt(3)\n\n-------------------------\n\nbut if you mean\n\n7x^2 - 2x - 2 = 0\n7x^2 - 2x = 2\nx^2 - (2/7)x = (2/7)\nx^2 - (2/7)x + (1/49) = (63/49)\n(x - (1/7))^2 = (9/7)\nx - (1/7) = (3/7)sqrt(7)\nx = (1/7) ± (3/7)sqrt(7)\nx = (1/7)(1 ± 3sqrt(7))
259349
Solve by substitution.\nSolve for y^2 in the second equation by subtracting x^2 and 2x from both sides.\nx^2 + y^2 + 2x - x^2 - 2x = 19 - x^2 - 2x\ny^2 = 19 - x^2 - 2x  Now substitute this into the first equation in place of y^2\nx^2 + 2(19 - x^2 - 2x) = 33  Distribute the 2\nx^2 + 38 - 2x^2 - 4x = 33  Combine x^2 and -2x^2 and subtract 33 from both sides\n-x^2 - 4x + 5 = 0  Multiply both sides by negative one (I just do this because it is easier to factor when the x^2 is positive)\nx^2 + 4x - 5 = 0  Now factor\nWe are looking for factors of -5 that add up 4.  5 and -1 work because 5*(-1) = -5 and 5 - 1 = 4\nTherefore x^2 + 4x -5 = 0 becomes\n(x+5)(x-1) = 0  Set each part equal to 0\nx+5 = 0 or x-1 = 0\nTherefore,\nx = -5 or x = 1\nNow substitute each of these values into the y^2 equation from above.\ny^2 = 19 - x^2 - 2x\nFor x = -5\ny^2 = 19 - (-5)^2 - 2(-5)\ny^2 = 19 - 25 + 10\ny^2 = 4  Take the square root of each side to get\ny = -2 or 2\n\nFor x = 1\ny^2 = 19 - (1)^2 - 2(1)\ny^2 = 19 - 1 - 2\nY^2 = 16  Take the square root of each side to get\ny = -4 or 4\n\nThus, the solutions are\n(-5,-2), (-5,2), (1,-4), (1,4)\n\nIt is always good to check your answers, especially on a test.  To check your answers just plug each one into each equation to see if you get a true statement.
781653
Eliminate the y to get\n2-x^2=2x+4\nx^2+2x+2=0\nusing quadratic formula\n(-2+-sqrt(4-4*2))/2\nwe see there are no real roots: the two functions do not intersect\nx= -1+-i
612346
Fact or out the x. This leaves 36x^2-84x+49 which is a perfect square (6x-7) so it facotrs to:\n\nx(6x-7)(6x-7)
1133153
7 - 2[4-6+2x] - 8+ x=6\n\n7 - 2[-2+2x] - 8 +x =6\n7 + 4 - 4x - 8 + x =6\n3 - 3x = 6\nx = -1\n\nDon't listen to the math goober - plug the value in and check it.
175133
2x-1(xsquared-x+10)squared
288929
-> 2x^2 - 1 = 4x + 15\n-> 2x^2 - 1 - 4x - 15 = 0\n-> 2x^2 -4x -16 = 0\n-> 2( x^2 -2x -8 )= 0\n-> x^2 - 2x - 8 = 0\n-> factoring the equation you will come up with\n-> (x - 4)(x + 2) = 0\n-> equate both factors to zero\n-> x - 4 =0 , x + 2 = 0\n-> x = 4, x = -2
784758
x^2+x+1=0\nx^2+2(1/2)x+1=0\nX^2+2(1/2)x+(1/2)^2+1-(1/2)^2=0\n(x+1/2)^2+3/4=0\n(x+1/2)^2=-3/4\nx=-1/2+/-√(3/4) i=-1/2+/-√3 * i/2
1054159
First, get rid of the brackets (multiply the terms inside the brackets by -1):\n\n7-2x^2 +2x -2 -2x -5 +2x^2\n\nCollect like terms:\n\n2x^2 -2x^2 +2x -2x +7-2-5 = 0\n\nIt's easy to see the sum is zero.
323064
x^2 + y^2 -6y = 7\n\nFirst complete the square of the y term\n\nx^2 + y^2 -6y + 9 = 7 + 9\n\nFactor\nx^2 + (y - 3)^2 = 16\n\nThis of the form (x-h)^2 + (y-k)^2 = r^2\n\nSo h = 0, k = 3, r = 4\n\nCenter is at (0,3) with radius 4.
871875
x+y=-7\nxy=60\n\n(x+y)^2=x^2+2xy+y^2\n49=x^2+y^2+120\n-71=x^2+y^2\nx^2>=0 and y^2>=0\nso I don't think there is a solution\n\nif their sum is -7 and their product is -60... then 5 and -12 are your numbers
844053
I'll rewrite the question for you, because we usually denote ^ as "to the power of" for simplicity.\n\nx^2 + y^2 - 4x + 2y = 4\n\nWe have to do a process called completing the square, for both the x and y variables.  So first, let's group all the x terms together and y terms together.\n\nx^2 - 4x + y^2 + 2y = 4\n\nTo complete the square, we have to add 4 to the x terms and 1 to the y terms.  Since we're adding 4 and 1 to the left hand side, we have to do the same to the right hand side.\n\nx^2 - 4x + 4 + y^2 + 2y + 1 = 4 + 4 + 1\n\nNow, we factor those now square polynomials.\n(x-2)^2 + (y+1)^2 = 9\n\nThe center of the circle is given by the values in the brackets, but the negative of them.  In the above case, the center is at (2,-1), since you take the negative of -2 (the value next to the x) and 1 (the value next to the y).\n\nTo get the radius, you take the square root of the right hand side, so the square root of 9 is 3.
957759
a. 0 = 7-x^2, x^2=7, x = +/-sqrt(7)\nArea = Integral[-sqrt(7), sqrt(7)] (7-x^2)dx = 7x - (1/3)x^3 |-sqrt(7), sqrt(7) = 2[7sqrt(7) - (1/3)sqrt(7)^3] ~= 24.69 u^2\n\nb. 0 = x^4-8, x^4 = 8, x = +/-8^(1/4)\nArea = (1/5)x^5-8x |-8^(1/4), 8^(1/4) = 2[(1/5)8^(5/4)-8(8)^(1/4)] ~absv= 21.53 u^2
239483
zero  you said squared, not to the zero power.  0^2=0  try it on your calculator.
1187142
maybe something like 7^(1/3) over 7^(1/2)\n\nthat's the same as the cube root of 7 over the square root of 7.\nTo solve it, you would just subtract the exponents and you'd get 1 over 7^(1/6)\n\nI hope that is what you are looking for.
869879
Complete the square:\nx^2 - 4x + 4 + y^2 + 6y + 9 = 12+4+9\n(x-2)^2 + (y+3)^2 = 25 = 5^2\nRadius 5, centre (2,-3).
832801
Completing the square involves adding constants to both sides of your equation so you have a form:\n\n(x - a)^2 = b\n\nOnce you get this form, you can take the square root of both sides:\n\nx - a = sqrt(b)\n\nx = a + sqrt(b) \n\nSince a square root can be either positive or negative, it is just as correct to write:\n\nx = a - sqrt(b)\n\nNow, back to the original "perfect square"\n\n(x - a)^2 = b\n\nExpanding this out:\n\nx^2 - 2*a + a^2 = b\n\nMoving b to the other side:\n\nx^2 - 2*a + a^2 - b = 0\n\nYour equation is 2*x^2 - x - 2 = 0\n\nForst thing is to get plain x^2, so divide by 2:\n\nx^2 - (1/2) * x - 1 = 0\n\nNow from the form above, a = 1/.4 because 2*a = (1/2)*x\nNext, look at the constant term: \n \n-1 = a^2 - b\n-1 = (1/4)^2 - b\n\nSolving for b: b = 17/16\n\nSo your perfect square equation is:\n\n(x - 1/4)^2 = 17/16\n\nSolving for x:\n\nx - 1/4 = sqrt(17/16)\n\nx = 1/4 + sqrt(17/16)\nx = 1/4 - sqrt(17/16)\n\nSimplifying slightly:\n\nx = (1 + sqrt(17))/4\nx = (1 - sqrt(17))/4