Expanding the left side:
(2x+7)(2x-7) + 30
= 4x^2 - 14x + 14x - 49 + 30= 4x^2 - 19
Expanding the right side:
6x(1-x)
= 6x - 6x^2
Setting both sides equal to each other:
4x^2 - 19 = 6x - 6x^2
Rearranging the equation:
4x^2 + 6x^2 - 6x - 19 - 6x = 010x^2 - 12x - 19 = 0
This is a quadratic equation that can be solved using the quadratic formula:
x = (-(-12) ± √((-12)^2 - 410(-19))) / 2*10x = (12 ± √(144 + 760)) / 20x = (12 ± √904) / 20x = (12 ± 30.066) / 20
Therefore, the solutions for x are:
x = (12 + 30.066) / 20 = 42.066 / 20 = 2.10
or
x = (12 - 30.066) / 20 = -18.066 / 20 = -0.90
So the solutions for the equation are x = 2.10 and x = -0.90.
Expanding the left side:
(2x+7)(2x-7) + 30
= 4x^2 - 14x + 14x - 49 + 30
= 4x^2 - 19
Expanding the right side:
6x(1-x)
= 6x - 6x^2
Setting both sides equal to each other:
4x^2 - 19 = 6x - 6x^2
Rearranging the equation:
4x^2 + 6x^2 - 6x - 19 - 6x = 0
10x^2 - 12x - 19 = 0
This is a quadratic equation that can be solved using the quadratic formula:
x = (-(-12) ± √((-12)^2 - 410(-19))) / 2*10
x = (12 ± √(144 + 760)) / 20
x = (12 ± √904) / 20
x = (12 ± 30.066) / 20
Therefore, the solutions for x are:
x = (12 + 30.066) / 20 = 42.066 / 20 = 2.10
or
x = (12 - 30.066) / 20 = -18.066 / 20 = -0.90
So the solutions for the equation are x = 2.10 and x = -0.90.