Solve 7^2-3.95^2=x^2

$${ 7 }^{ 2 } - { 3.95 }^{ 2 } = { x }^{ 2 }$$

Solve for x

$$x = \frac{\sqrt{13359}}{20} \approx 5.779057017$$

$$x = -\frac{\sqrt{13359}}{20} \approx -5.779057017$$

Steps by Finding Square Root

Calculate 7 to the power of 2 and get 49.

$$49-3.95^{2}=x^{2}$$

Calculate 3.95 to the power of 2 and get 15.6025.

$$49-15.6025=x^{2}$$

Subtract 15.6025 from 49 to get 33.3975.

$$33.3975=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=33.3975$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{13359}}{20} x=-\frac{\sqrt{13359}}{20}$$

Steps Using the Quadratic Formula

Calculate 7 to the power of 2 and get 49.

$$49-3.95^{2}=x^{2}$$

Calculate 3.95 to the power of 2 and get 15.6025.

$$49-15.6025=x^{2}$$

Subtract 15.6025 from 49 to get 33.3975.

$$33.3975=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=33.3975$$

Subtract 33.3975 from both sides.

$$x^{2}-33.3975=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -33.3975 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-33.3975\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-33.3975\right)}}{2}$$

Multiply -4 times -33.3975.

$$x=\frac{0±\sqrt{133.59}}{2}$$

Take the square root of 133.59.

$$x=\frac{0±\frac{\sqrt{13359}}{10}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{13359}}{10}}{2} when ± is plus.

$$x=\frac{\sqrt{13359}}{20}$$

Now solve the equation x=\frac{0±\frac{\sqrt{13359}}{10}}{2} when ± is minus.

$$x=-\frac{\sqrt{13359}}{20}$$

The equation is now solved.

$$x=\frac{\sqrt{13359}}{20} x=-\frac{\sqrt{13359}}{20}$$