Solve (x-4)(x+4)=7

$$(x-4)(x+4)=7$$

Solve for x

$$x=\sqrt{23}\approx 4.795831523$$

$$x=-\sqrt{23}\approx -4.795831523$$

Steps by Finding Square Root

Consider \left(x-4\right)\left(x+4\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 4.

$$x^{2}-16=7$$

Add 16 to both sides.

$$x^{2}=7+16$$

Add 7 and 16 to get 23.

$$x^{2}=23$$

Take the square root of both sides of the equation.

$$x=\sqrt{23} x=-\sqrt{23}$$

Steps Using the Quadratic Formula

Consider \left(x-4\right)\left(x+4\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 4.

$$x^{2}-16=7$$

Subtract 7 from both sides.

$$x^{2}-16-7=0$$

Subtract 7 from -16 to get -23.

$$x^{2}-23=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -23 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-23\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-23\right)}}{2}$$

Multiply -4 times -23.

$$x=\frac{0±\sqrt{92}}{2}$$

Take the square root of 92.

$$x=\frac{0±2\sqrt{23}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{23}}{2} when ± is plus.

$$x=\sqrt{23}$$

Now solve the equation x=\frac{0±2\sqrt{23}}{2} when ± is minus.

$$x=-\sqrt{23}$$

The equation is now solved.

$$x=\sqrt{23} x=-\sqrt{23}$$