Solve A=(2x-3)^2-(-x-3)^2+5=

$$A = ( 2 x - 3 ) ^ { 2 } - ( - x - 3 ) ^ { 2 } + 5 =$$

Solve for A

$$A=3x\left(x-6\right)+5$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3\right)^{2}.

$$A=4x^{2}-12x+9-\left(-x-3\right)^{2}+5$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-x-3\right)^{2}.

$$A=4x^{2}-12x+9-\left(\left(-x\right)^{2}-6\left(-x\right)+9\right)+5$$

Calculate -x to the power of 2 and get x^{2}.

$$A=4x^{2}-12x+9-\left(x^{2}-6\left(-x\right)+9\right)+5$$

Multiply -6 and -1 to get 6.

$$A=4x^{2}-12x+9-\left(x^{2}+6x+9\right)+5$$

To find the opposite of x^{2}+6x+9, find the opposite of each term.

$$A=4x^{2}-12x+9-x^{2}-6x-9+5$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$A=3x^{2}-12x+9-6x-9+5$$

Combine -12x and -6x to get -18x.

$$A=3x^{2}-18x+9-9+5$$

Subtract 9 from 9 to get 0.

$$A=3x^{2}-18x+5$$

Solve for x (complex solution)

$$x=\frac{\sqrt{3A+66}}{3}+3$$

$$x=-\frac{\sqrt{3A+66}}{3}+3$$

Solve for x

$$x=\frac{\sqrt{3A+66}}{3}+3$$

$$x=-\frac{\sqrt{3A+66}}{3}+3\text{, }A\geq -22$$