Solve x^2+5^2=6.8^2

$$x ^ { 2 } + 5 ^ { 2 } = 6.8 ^ { 2 }$$

Solve for x

$$x = \frac{3 \sqrt{59}}{5} \approx 4.608687449$$

$$x = -\frac{3 \sqrt{59}}{5} \approx -4.608687449$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$x^{2}+25=6.8^{2}$$

Calculate 6.8 to the power of 2 and get 46.24.

$$x^{2}+25=46.24$$

Subtract 25 from both sides.

$$x^{2}=46.24-25$$

Subtract 25 from 46.24 to get 21.24.

$$x^{2}=21.24$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{59}}{5} x=-\frac{3\sqrt{59}}{5}$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$x^{2}+25=6.8^{2}$$

Calculate 6.8 to the power of 2 and get 46.24.

$$x^{2}+25=46.24$$

Subtract 46.24 from both sides.

$$x^{2}+25-46.24=0$$

Subtract 46.24 from 25 to get -21.24.

$$x^{2}-21.24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -21.24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-21.24\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-21.24\right)}}{2}$$

Multiply -4 times -21.24.

$$x=\frac{0±\sqrt{84.96}}{2}$$

Take the square root of 84.96.

$$x=\frac{0±\frac{6\sqrt{59}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{6\sqrt{59}}{5}}{2} when ± is plus.

$$x=\frac{3\sqrt{59}}{5}$$

Now solve the equation x=\frac{0±\frac{6\sqrt{59}}{5}}{2} when ± is minus.

$$x=-\frac{3\sqrt{59}}{5}$$

The equation is now solved.

$$x=\frac{3\sqrt{59}}{5} x=-\frac{3\sqrt{59}}{5}$$