Solve x*x+1=208

$$x \cdot x + 1 = 208$$

Solve for x

$$x=3\sqrt{23}\approx 14.38749457$$

$$x=-3\sqrt{23}\approx -14.38749457$$

Steps by Finding Square Root

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

$$x^{2}+1=208$$

Subtract 1 from both sides.

$$x^{2}=208-1$$

Subtract 1 from 208 to get 207.

$$x^{2}=207$$

Take the square root of both sides of the equation.

$$x=3\sqrt{23} x=-3\sqrt{23}$$

Steps Using the Quadratic Formula

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

$$x^{2}+1=208$$

Subtract 208 from both sides.

$$x^{2}+1-208=0$$

Subtract 208 from 1 to get -207.

$$x^{2}-207=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -207 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-207\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-207\right)}}{2}$$

Multiply -4 times -207.

$$x=\frac{0±\sqrt{828}}{2}$$

Take the square root of 828.

$$x=\frac{0±6\sqrt{23}}{2}$$

Now solve the equation x=\frac{0±6\sqrt{23}}{2} when ± is plus.

$$x=3\sqrt{23}$$

Now solve the equation x=\frac{0±6\sqrt{23}}{2} when ± is minus.

$$x=-3\sqrt{23}$$

The equation is now solved.

$$x=3\sqrt{23} x=-3\sqrt{23}$$