m^2 + m - 42=0 ?, n^2 - 8n + 7 =0?, x^2 + 6x + 5=0?, x^2 - 9x + 14 =0?
361234
(m-6)(m+7)=0\nm=6 or m=-7\n\n(n-1)(n-7)=0\nn=1 or n=7\n\n(x+1)(x+5)=0\nx=-1 or x=-5\n\n(x-2)(x-7)=0\nx=2 or x=7\n\nas easy as ABC!!!
52440
[x+1]/x^2+10x+5=2x/x^2+x-2\n9x+7=[x+1]/x^2\n9x^3+7x^2=x+1\n9x^3+7x^2-x=1
657080
(x + 1)^2 = 25\nx + 1 = -5 or 5\nx = -6 or 4\n\n---------------------\n\nx^2 + 4x + 4 = 16\nx^2 + 4x - 12 = 0\n(x + 6)(x - 2) = 0\nx = -6 or 2\n\n----------------------\n\nx^2 - 14x + 49 = 13\nx^2 - 14x + 36 = 0\n\nx = (-b ± sqrt(b^2 - 4ac))/2a\nx = (-(-14) ± sqrt((-14)^2 - 4(1)(36)))/2(1)\nx = (14 ± sqrt(196 - 144))/2\nx = (14 ± sqrt(52))/2\nx = (14 ± sqrt(4 * 13))/2\nx = (14 ± 2sqrt(13))/2\nx = 7 ± sqrt(13)
301645
If you have an equation like 5x^2 + 7x - 6 = 0:\n\nGet the x^2 term by itself\nx^2 + 7x/5 - 6/5 = 0\n\nMove the constant to the other side\nx^2 + 7x/5 = 6/5\n\nTake half of the coefficient for the x term and square it: half of 7/5 is 7/10, squared is 49/100. Add this to both sides of the equation\n\nx^2 + 7x/5 + 49/100 = 6/5 + 49/100\nx^2 + 7x/5 + 49/100 = 169/100\n\nThe left side is a perfect square trinomial - factor it\n(x + 7/10)^2 = 169/100\n\nTake the square root of both sides and solve for x\nx + 7/10 = +/- 13/10\nx = -7/10 +/- 13/10\nx = 6/10 or -20/10\nx = 0.6 or -2
917843
(x + i)(x - i)(x - 3 + i)(x - 3 - i) = 0\n\n(x^2 - i^2)[(x - 3)^2 - i^2] = 0\n\n(x^2 + 1)(x^2 - 6x + 9 + 1) = 0\n\nx^4 - 6x^3 + 10x^2 + x^2 - 6x + 10 = 0\n\nx^4 - 6x^3 + 11x^2 - 6x + 10 = 0   (Answer)
65662
the above answer is wrong.\n\n( x^2 + 7x - 4 ) + ( x^2 + 9 ) = x^2 + x^2 + 7x -4 +9\n= 2x^2 + 7x + 5
1157065
(x+5)(2x^2+4x+2)\nx(2x^2+4x+2)+5(2x^2+4x+2)\n2x^3+4x^2+2x+10x^2+20x+10\n2x^3+14x^2+22x+10
785246
x^2-16=0\n(x+4)(x-4)=0\nx+4=0\nx=-4\n\nx-4=0\nx=-4\n\nx^3+14x^2+40x=0\nx(x^2-14x+40)=0\nx(x-10)(x-4)=0\nx=0\n\nx-10=0\nx=10\n\nx-4=0\nx=4\n\nx^4-5x^2+4=0\n(x^2-4)(x^2-1)=0\n(x-2)(x+2)(x-1)(x+1)=0\nxi2=0\nx=2\nx+2=0\nx=-2\nx-1=0\nx=1\nx+1=0\nx=-1
919399
6(x+4)-2x=-8\n6x+24-2x=-8\n6x-2x+24+8=0\n4x+32=0\n4x=-32\nx=-32/4\nx=-8
694839
(y+4)(y+4)-2y -11=0\ny^2 +8y + 16 -2y -11 =0\ny^2 +6y +5=0\n(y+5)(y+1)=0\ny=-5, x=-1 , and   y=-1, x=3\n\nCheck with y=-5\n(-1)^2 -2(-5) = 1+10=11  OK\n\nCheck with y=-1\n3^2 -2(-1) = 9+2=11  OK
887085
First, I multiplied the first equation by 2 and the second one by -5 in order to make it easy for me to cancel out both x's.\n2(-5x+7y=-40)\n-5(-2x+4y=-16)\n\n-10x+14y=-80\n10x+-20y=80\n\nNow, you can actually cancel out the x's and the constants at the end.\n\n-6y=0\ny=0\n\nNow you plug y=0 into one of the equations to find x.\n\n-5x + 7(0) = -40\n-5x +0 = -40\n-5x = -40\nx = 8\n\n(0,8) is the answer.
707418
20x^2+60x + 45\n= 5(4x^2+12x + 9) \n= 5((2x)^2+2(2x)3+3^2) = 5(2x+3)^2\n\n3x^2+12x+12 = 0\n=> x^2+4x+4 = 0 (divide by 4)\n=>(x+2) ^2 = 0 or x = -2, -2 (double root)\n\n7x^2-28 =0\n= x^2 = 4\n=> x = 2 or -2\n\narea = xy = 5*2 = 10cm^2
919015
(8X^6/7) * (56/24)\n8X^6/3\n\n(Hint:  X^m/X^n = X^(m-n)
786009
-2(x-3) + 4(x+7)\n-2x+6   +4x+28\n2x+34
776908
complete the square:\n\ny= -2x^2-4x-7\n\ny= -2(x^2 + 2x + 7/2)\ny = -2(x^2 + 2x + 7/2) + -2(-5/2) + 2(-5/2)\ny = -2(x^2 + 2x + 7/2 -5/2) + 2(-5/2)\ny = -2(x^2 + 2x + 1) - 5\ny = -2(x + 1)^2 -5\n\nThe other way to do it is to use the formula:\nax^2 + bx + c = a(x + (b/2a))^2 + c - (b^2/4a)\n\nwhich also yields -2(x + 1)^2 - 5.\n\nYour answer is correct.
17048
= x^2 - 7x + 4x -28\n= x^2 - 3x - 28
775457
multiplying by x\nx^2-5=4x\nx^2-4x-5=0\n(x-5)(x+1)=0\nx=5 or -1