Solve x^2=1^2+3^2

$$x ^ { 2 } = 1 ^ { 2 } + 3 ^ { 2 }$$

Solve for x

$$x=\sqrt{10}\approx 3.16227766$$

$$x=-\sqrt{10}\approx -3.16227766$$

Steps by Finding Square Root

Calculate 1 to the power of 2 and get 1.

$$x^{2}=1+3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}=1+9$$

Add 1 and 9 to get 10.

$$x^{2}=10$$

Take the square root of both sides of the equation.

$$x=\sqrt{10} x=-\sqrt{10}$$

Steps Using the Quadratic Formula

Calculate 1 to the power of 2 and get 1.

$$x^{2}=1+3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}=1+9$$

Add 1 and 9 to get 10.

$$x^{2}=10$$

Subtract 10 from both sides.

$$x^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-10\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-10\right)}}{2}$$

Multiply -4 times -10.

$$x=\frac{0±\sqrt{40}}{2}$$

Take the square root of 40.

$$x=\frac{0±2\sqrt{10}}{2}$$

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

$$x=\sqrt{10}$$

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

$$x=-\sqrt{10}$$

The equation is now solved.

$$x=\sqrt{10} x=-\sqrt{10}$$