Solve 2(2x-1)^2-9=c

$$2 ( 2 x - 1 ) ^ { 2 } - 9 = c$$

Solve for c

$$c=2\left(2x-1\right)^{2}-9$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-1\right)^{2}.

$$2\left(4x^{2}-4x+1\right)-9=c$$

Use the distributive property to multiply 2 by 4x^{2}-4x+1.

$$8x^{2}-8x+2-9=c$$

Subtract 9 from 2 to get -7.

$$8x^{2}-8x-7=c$$

Swap sides so that all variable terms are on the left hand side.

$$c=8x^{2}-8x-7$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2c+18}}{4}+\frac{1}{2}$$

$$x=\frac{\sqrt{2c+18}}{4}+\frac{1}{2}$$

Solve for x

$$x=-\frac{\sqrt{2c+18}}{4}+\frac{1}{2}$$

$$x=\frac{\sqrt{2c+18}}{4}+\frac{1}{2}\text{, }c\geq -9$$