Solve 14.8=x^2+x^2

$$14.8= { x }^{ 2 } + { x }^{ 2 }$$

Solve for x

$$x = \frac{\sqrt{185}}{5} \approx 2.720294102$$

$$x = -\frac{\sqrt{185}}{5} \approx -2.720294102$$

Steps by Finding Square Root

Combine x^{2} and x^{2} to get 2x^{2}.

$$14.8=2x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}=14.8$$

Divide both sides by 2.

$$x^{2}=\frac{14.8}{2}$$

Expand \frac{14.8}{2} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{148}{20}$$

Reduce the fraction \frac{148}{20} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{37}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{185}}{5} x=-\frac{\sqrt{185}}{5}$$

Steps Using the Quadratic Formula

Combine x^{2} and x^{2} to get 2x^{2}.

$$14.8=2x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}=14.8$$

Subtract 14.8 from both sides.

$$2x^{2}-14.8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -14.8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-14.8\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-14.8\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-14.8\right)}}{2\times 2}$$

Multiply -8 times -14.8.

$$x=\frac{0±\sqrt{118.4}}{2\times 2}$$

Take the square root of 118.4.

$$x=\frac{0±\frac{4\sqrt{185}}{5}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±\frac{4\sqrt{185}}{5}}{4}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{185}}{5}}{4} when ± is plus.

$$x=\frac{\sqrt{185}}{5}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{185}}{5}}{4} when ± is minus.

$$x=-\frac{\sqrt{185}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{185}}{5} x=-\frac{\sqrt{185}}{5}$$