46
Improved answer:
First rearrange this quadratic equation which will have two solutions :
2x2-10x-6 = 0
Simplify the equation by dividing all terms by 2:
x2-5x-3 = 0
Then by using the quadratic equation formula it will work out as:
x = (5 + the square root of 37)/2
or x = (5 - the square root of 37)/2
2x2 = 10x + 12 2x2 - 10x - 12 = 0 x2 -5x -6 = 0 x2 - 6x + x - 6 = 0 x(x -6) + 1(x -6) = 0 (x+1)(x-6) = 0 x = -1 or x = 6
x + 13x + 10x = 50 - 6
6-x+12 = 10x+7 6+12-7 = 10x+x 11 = 11x x = 1
x2 + 7x = 2x2 + 6 x2 - 2x2 + 7x = 6 -x2 +7x - 6 = 0 or alternatively x2 - 7x + 6 = 0
-6x-6 -or- -6(x+1)
2x2 = 10x + 12 2x2 - 10x - 12 = 0 x2 -5x -6 = 0 x2 - 6x + x - 6 = 0 x(x -6) + 1(x -6) = 0 (x+1)(x-6) = 0 x = -1 or x = 6
x + 13x + 10x = 50 - 6
6-x+12 = 10x+7 6+12-7 = 10x+x 11 = 11x x = 1
x2 + 7x = 2x2 + 6 x2 - 2x2 + 7x = 6 -x2 +7x - 6 = 0 or alternatively x2 - 7x + 6 = 0
-6x-6 -or- -6(x+1)
y=-10x-4
20x3 - 70x2 + 60x = 10x(2x2 - 7x + 6) = 10x(2x - 3)(x - 2).
6-3x = 5x-10x+2 4 = 8x-10x 4 = -2x x = -2
12x - 6 = 10x +2 12x - 10x = 2 + 6 2x = 8 x = 4
-6
10*6+8*7 = 116
I'm going to assume you mean F(x) = -2x2 + 10x + 6 as -2x plus 10x = 8x...First differentiate -2x2 + 10x + 6:dy/dx = -4x + 10Set dy/dx = 0:-4x + 10 = 0Find x:10 = 4x2.5 = xFind y at x =2.5:y = -2(2.5)2 + 10(2.5) + 6 = -12.5 + 25 +6 = 18.5So max or min is at (2.5, 18.5)To find out whether it is max or min differentiate twice:d2y/dx2 = -4If its negative, point will be a maximumIf its positive, point will be a minimum.In this case, a maximum occurs at (2.5, 18.5).