Solve A=(7x+8)(7x-8)

$$A = ( 7 x + 8 ) ( 7 x - 8 )$$

Solve for A

$$A=49x^{2}-64$$

Solution Steps

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

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

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

$$A=7^{2}x^{2}-64$$

Calculate 7 to the power of 2 and get 49.

$$A=49x^{2}-64$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{A+64}}{7}$$

$$x=\frac{\sqrt{A+64}}{7}$$

Solve for x

$$x=-\frac{\sqrt{A+64}}{7}$$

$$x=\frac{\sqrt{A+64}}{7}\text{, }A\geq -64$$