Solve (x-8)(x+8)=17

$$( x - 8 ) ( x + 8 ) = 17$$

Solve for x

$$x=-9$$

$$x=9$$

Steps by Finding Square Root

Consider \left(x-8\right)\left(x+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.

$$x^{2}-64=17$$

Add 64 to both sides.

$$x^{2}=17+64$$

Add 17 and 64 to get 81.

$$x^{2}=81$$

Take the square root of both sides of the equation.

$$x=9 x=-9$$

Steps Using the Quadratic Formula

Consider \left(x-8\right)\left(x+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.

$$x^{2}-64=17$$

Subtract 17 from both sides.

$$x^{2}-64-17=0$$

Subtract 17 from -64 to get -81.

$$x^{2}-81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-81\right)}}{2}$$

Multiply -4 times -81.

$$x=\frac{0±\sqrt{324}}{2}$$

Take the square root of 324.

$$x=\frac{0±18}{2}$$

Now solve the equation x=\frac{0±18}{2} when ± is plus. Divide 18 by 2.

$$x=9$$

Now solve the equation x=\frac{0±18}{2} when ± is minus. Divide -18 by 2.

$$x=-9$$

The equation is now solved.

$$x=9 x=-9$$