Solve x^2+1=164

$$x ^ { 2 } + 1 = 164$$

Solve for x

$$x=\sqrt{163}\approx 12.767145335$$

$$x=-\sqrt{163}\approx -12.767145335$$

Steps by Finding Square Root

Subtract 1 from both sides.

$$x^{2}=164-1$$

Subtract 1 from 164 to get 163.

$$x^{2}=163$$

Take the square root of both sides of the equation.

$$x=\sqrt{163} x=-\sqrt{163}$$

Steps Using the Quadratic Formula

Subtract 164 from both sides.

$$x^{2}+1-164=0$$

Subtract 164 from 1 to get -163.

$$x^{2}-163=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -163 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-163\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-163\right)}}{2}$$

Multiply -4 times -163.

$$x=\frac{0±\sqrt{652}}{2}$$

Take the square root of 652.

$$x=\frac{0±2\sqrt{163}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{163}}{2} when ± is plus.

$$x=\sqrt{163}$$

Now solve the equation x=\frac{0±2\sqrt{163}}{2} when ± is minus.

$$x=-\sqrt{163}$$

The equation is now solved.

$$x=\sqrt{163} x=-\sqrt{163}$$