Solve x^2+4=103

$${ x }^{ 2 } +4=103$$

Solve for x

$$x=3\sqrt{11}\approx 9.949874371$$

$$x=-3\sqrt{11}\approx -9.949874371$$

Steps by Finding Square Root

Subtract 4 from both sides.

$$x^{2}=103-4$$

Subtract 4 from 103 to get 99.

$$x^{2}=99$$

Take the square root of both sides of the equation.

$$x=3\sqrt{11} x=-3\sqrt{11}$$

Steps Using the Quadratic Formula

Subtract 103 from both sides.

$$x^{2}+4-103=0$$

Subtract 103 from 4 to get -99.

$$x^{2}-99=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -99 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-99\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-99\right)}}{2}$$

Multiply -4 times -99.

$$x=\frac{0±\sqrt{396}}{2}$$

Take the square root of 396.

$$x=\frac{0±6\sqrt{11}}{2}$$

Now solve the equation x=\frac{0±6\sqrt{11}}{2} when ± is plus.

$$x=3\sqrt{11}$$

Now solve the equation x=\frac{0±6\sqrt{11}}{2} when ± is minus.

$$x=-3\sqrt{11}$$

The equation is now solved.

$$x=3\sqrt{11} x=-3\sqrt{11}$$