Solve x^2=2*5^2+6^2

$$x ^ { 2 } = 2 \cdot 5 ^ { 2 } + 6 ^ { 2 }$$

Solve for x

$$x=\sqrt{86}\approx 9.273618495$$

$$x=-\sqrt{86}\approx -9.273618495$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$x^{2}=2\times 25+6^{2}$$

Multiply 2 and 25 to get 50.

$$x^{2}=50+6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$x^{2}=50+36$$

Add 50 and 36 to get 86.

$$x^{2}=86$$

Take the square root of both sides of the equation.

$$x=\sqrt{86} x=-\sqrt{86}$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$x^{2}=2\times 25+6^{2}$$

Multiply 2 and 25 to get 50.

$$x^{2}=50+6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$x^{2}=50+36$$

Add 50 and 36 to get 86.

$$x^{2}=86$$

Subtract 86 from both sides.

$$x^{2}-86=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -86 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-86\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-86\right)}}{2}$$

Multiply -4 times -86.

$$x=\frac{0±\sqrt{344}}{2}$$

Take the square root of 344.

$$x=\frac{0±2\sqrt{86}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{86}}{2} when ± is plus.

$$x=\sqrt{86}$$

Now solve the equation x=\frac{0±2\sqrt{86}}{2} when ± is minus.

$$x=-\sqrt{86}$$

The equation is now solved.

$$x=\sqrt{86} x=-\sqrt{86}$$