Solve x^2+28=78

$${ x }^{ 2 } +28=78$$

Solve for x

$$x=5\sqrt{2}\approx 7.071067812$$

$$x=-5\sqrt{2}\approx -7.071067812$$

Steps by Finding Square Root

Subtract 28 from both sides.

$$x^{2}=78-28$$

Subtract 28 from 78 to get 50.

$$x^{2}=50$$

Take the square root of both sides of the equation.

$$x=5\sqrt{2} x=-5\sqrt{2}$$

Steps Using the Quadratic Formula

Subtract 78 from both sides.

$$x^{2}+28-78=0$$

Subtract 78 from 28 to get -50.

$$x^{2}-50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-50\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-50\right)}}{2}$$

Multiply -4 times -50.

$$x=\frac{0±\sqrt{200}}{2}$$

Take the square root of 200.

$$x=\frac{0±10\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±10\sqrt{2}}{2} when ± is plus.

$$x=5\sqrt{2}$$

Now solve the equation x=\frac{0±10\sqrt{2}}{2} when ± is minus.

$$x=-5\sqrt{2}$$

The equation is now solved.

$$x=5\sqrt{2} x=-5\sqrt{2}$$