Solve x^2=2.4^2+2.8^2

$${ x }^{ 2 } = { 2.4 }^{ 2 } + { 2.8 }^{ 2 }$$

Solve for x

$$x = \frac{2 \sqrt{85}}{5} \approx 3.687817783$$

$$x = -\frac{2 \sqrt{85}}{5} \approx -3.687817783$$

Steps by Finding Square Root

Calculate 2.4 to the power of 2 and get 5.76.

$$x^{2}=5.76+2.8^{2}$$

Calculate 2.8 to the power of 2 and get 7.84.

$$x^{2}=5.76+7.84$$

Add 5.76 and 7.84 to get 13.6.

$$x^{2}=13.6$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{85}}{5} x=-\frac{2\sqrt{85}}{5}$$

Steps Using the Quadratic Formula

Calculate 2.4 to the power of 2 and get 5.76.

$$x^{2}=5.76+2.8^{2}$$

Calculate 2.8 to the power of 2 and get 7.84.

$$x^{2}=5.76+7.84$$

Add 5.76 and 7.84 to get 13.6.

$$x^{2}=13.6$$

Subtract 13.6 from both sides.

$$x^{2}-13.6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -13.6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-13.6\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-13.6\right)}}{2}$$

Multiply -4 times -13.6.

$$x=\frac{0±\sqrt{54.4}}{2}$$

Take the square root of 54.4.

$$x=\frac{0±\frac{4\sqrt{85}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{85}}{5}}{2} when ± is plus.

$$x=\frac{2\sqrt{85}}{5}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{85}}{5}}{2} when ± is minus.

$$x=-\frac{2\sqrt{85}}{5}$$

The equation is now solved.

$$x=\frac{2\sqrt{85}}{5} x=-\frac{2\sqrt{85}}{5}$$