Solve 10*x^2+5^2=(5sqrt{2})^2

$$10 \cdot x ^ { 2 } + 5 ^ { 2 } = ( 5 \sqrt { 2 } ) ^ { 2 }$$

Solve for x

$$x = \frac{\sqrt{10}}{2} \approx 1.58113883$$

$$x = -\frac{\sqrt{10}}{2} \approx -1.58113883$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$10x^{2}+25=\left(5\sqrt{2}\right)^{2}$$

Expand \left(5\sqrt{2}\right)^{2}.

$$10x^{2}+25=5^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$10x^{2}+25=25\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$10x^{2}+25=25\times 2$$

Multiply 25 and 2 to get 50.

$$10x^{2}+25=50$$

Subtract 25 from both sides.

$$10x^{2}=50-25$$

Subtract 25 from 50 to get 25.

$$10x^{2}=25$$

Divide both sides by 10.

$$x^{2}=\frac{25}{10}$$

Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{5}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{10}}{2} x=-\frac{\sqrt{10}}{2}$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$10x^{2}+25=\left(5\sqrt{2}\right)^{2}$$

Expand \left(5\sqrt{2}\right)^{2}.

$$10x^{2}+25=5^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$10x^{2}+25=25\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$10x^{2}+25=25\times 2$$

Multiply 25 and 2 to get 50.

$$10x^{2}+25=50$$

Subtract 50 from both sides.

$$10x^{2}+25-50=0$$

Subtract 50 from 25 to get -25.

$$10x^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 10\left(-25\right)}}{2\times 10}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 10\left(-25\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{0±\sqrt{-40\left(-25\right)}}{2\times 10}$$

Multiply -40 times -25.

$$x=\frac{0±\sqrt{1000}}{2\times 10}$$

Take the square root of 1000.

$$x=\frac{0±10\sqrt{10}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{0±10\sqrt{10}}{20}$$

Now solve the equation x=\frac{0±10\sqrt{10}}{20} when ± is plus.

$$x=\frac{\sqrt{10}}{2}$$

Now solve the equation x=\frac{0±10\sqrt{10}}{20} when ± is minus.

$$x=-\frac{\sqrt{10}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{10}}{2} x=-\frac{\sqrt{10}}{2}$$