Solve x^2+2.4^2=8^2

$$x ^ { 2 } + 2.4 ^ { 2 } = 8 ^ { 2 }$$

Solve for x

$$x = \frac{4 \sqrt{91}}{5} \approx 7.631513611$$

$$x = -\frac{4 \sqrt{91}}{5} \approx -7.631513611$$

Steps by Finding Square Root

Calculate 2.4 to the power of 2 and get 5.76.

$$x^{2}+5.76=8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$x^{2}+5.76=64$$

Subtract 5.76 from both sides.

$$x^{2}=64-5.76$$

Subtract 5.76 from 64 to get 58.24.

$$x^{2}=58.24$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{91}}{5} x=-\frac{4\sqrt{91}}{5}$$

Steps Using the Quadratic Formula

Calculate 2.4 to the power of 2 and get 5.76.

$$x^{2}+5.76=8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$x^{2}+5.76=64$$

Subtract 64 from both sides.

$$x^{2}+5.76-64=0$$

Subtract 64 from 5.76 to get -58.24.

$$x^{2}-58.24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -58.24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-58.24\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-58.24\right)}}{2}$$

Multiply -4 times -58.24.

$$x=\frac{0±\sqrt{232.96}}{2}$$

Take the square root of 232.96.

$$x=\frac{0±\frac{8\sqrt{91}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{91}}{5}}{2} when ± is plus.

$$x=\frac{4\sqrt{91}}{5}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{91}}{5}}{2} when ± is minus.

$$x=-\frac{4\sqrt{91}}{5}$$

The equation is now solved.

$$x=\frac{4\sqrt{91}}{5} x=-\frac{4\sqrt{91}}{5}$$