Solve x^2+6=54

$${ x }^{ 2 } +6 = 54$$

Solve for x

$$x=4\sqrt{3}\approx 6.92820323$$

$$x=-4\sqrt{3}\approx -6.92820323$$

Steps by Finding Square Root

Subtract 6 from both sides.

$$x^{2}=54-6$$

Subtract 6 from 54 to get 48.

$$x^{2}=48$$

Take the square root of both sides of the equation.

$$x=4\sqrt{3} x=-4\sqrt{3}$$

Steps Using the Quadratic Formula

Subtract 54 from both sides.

$$x^{2}+6-54=0$$

Subtract 54 from 6 to get -48.

$$x^{2}-48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-48\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-48\right)}}{2}$$

Multiply -4 times -48.

$$x=\frac{0±\sqrt{192}}{2}$$

Take the square root of 192.

$$x=\frac{0±8\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±8\sqrt{3}}{2} when ± is plus.

$$x=4\sqrt{3}$$

Now solve the equation x=\frac{0±8\sqrt{3}}{2} when ± is minus.

$$x=-4\sqrt{3}$$

The equation is now solved.

$$x=4\sqrt{3} x=-4\sqrt{3}$$