Solve H=(8x-7y)(8x+7y)

$$H = ( 8 x - 7 y ) ( 8 x + 7 y )$$

Solve for H

$$H=64x^{2}-49y^{2}$$

Solution Steps

Consider \left(8x-7y\right)\left(8x+7y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$H=\left(8x\right)^{2}-\left(7y\right)^{2}$$

Expand \left(8x\right)^{2}.

$$H=8^{2}x^{2}-\left(7y\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$H=64x^{2}-\left(7y\right)^{2}$$

Expand \left(7y\right)^{2}.

$$H=64x^{2}-7^{2}y^{2}$$

Calculate 7 to the power of 2 and get 49.

$$H=64x^{2}-49y^{2}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{49y^{2}+H}}{8}$$

$$x=\frac{\sqrt{49y^{2}+H}}{8}$$

Solve for x

$$x=-\frac{\sqrt{49y^{2}+H}}{8}$$

$$x=\frac{\sqrt{49y^{2}+H}}{8}\text{, }H\geq -49y^{2}$$