Solve x^2+x^2+1=25

$${ x }^{ 2 } + { x }^{ 2 } +1=25$$

Solve for x

$$x=2\sqrt{3}\approx 3.464101615$$

$$x=-2\sqrt{3}\approx -3.464101615$$

Steps by Finding Square Root

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

$$2x^{2}+1=25$$

Subtract 1 from both sides.

$$2x^{2}=25-1$$

Subtract 1 from 25 to get 24.

$$2x^{2}=24$$

Divide both sides by 2.

$$x^{2}=\frac{24}{2}$$

Divide 24 by 2 to get 12.

$$x^{2}=12$$

Take the square root of both sides of the equation.

$$x=2\sqrt{3} x=-2\sqrt{3}$$

Steps Using the Quadratic Formula

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

$$2x^{2}+1=25$$

Subtract 25 from both sides.

$$2x^{2}+1-25=0$$

Subtract 25 from 1 to get -24.

$$2x^{2}-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-24\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-24\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-24\right)}}{2\times 2}$$

Multiply -8 times -24.

$$x=\frac{0±\sqrt{192}}{2\times 2}$$

Take the square root of 192.

$$x=\frac{0±8\sqrt{3}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±8\sqrt{3}}{4}$$

Now solve the equation x=\frac{0±8\sqrt{3}}{4} when ± is plus.

$$x=2\sqrt{3}$$

Now solve the equation x=\frac{0±8\sqrt{3}}{4} when ± is minus.

$$x=-2\sqrt{3}$$

The equation is now solved.

$$x=2\sqrt{3} x=-2\sqrt{3}$$