Solve A/2=(x-3/4)^2-25/16

$$\frac { A } { 2 } = ( x - \frac { 3 } { 4 } ) ^ { 2 } - \frac { 25 } { 16 }$$

Solve for A

$$A=\left(x-2\right)\left(2x+1\right)$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 16, the least common multiple of 2,16.

$$8A=16\left(x-\frac{3}{4}\right)^{2}-25$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{3}{4}\right)^{2}.

$$8A=16\left(x^{2}-\frac{3}{2}x+\frac{9}{16}\right)-25$$

Use the distributive property to multiply 16 by x^{2}-\frac{3}{2}x+\frac{9}{16}.

$$8A=16x^{2}-24x+9-25$$

Subtract 25 from 9 to get -16.

$$8A=16x^{2}-24x-16$$

Divide both sides by 8.

$$\frac{8A}{8}=\frac{8\left(x-2\right)\left(2x+1\right)}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$A=\frac{8\left(x-2\right)\left(2x+1\right)}{8}$$

Divide 8\left(-2+x\right)\left(1+2x\right) by 8.

$$A=\left(x-2\right)\left(2x+1\right)$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{8A+25}+3}{4}$$

$$x=\frac{\sqrt{8A+25}+3}{4}$$

Solve for x

$$x=\frac{-\sqrt{8A+25}+3}{4}$$

$$x=\frac{\sqrt{8A+25}+3}{4}\text{, }A\geq -\frac{25}{8}$$