Solve 5x^2+7-55=0

$$5 { x }^{ 2 } +7-55=0$$

Solve for x

$$x = \frac{4 \sqrt{15}}{5} \approx 3.098386677$$

$$x = -\frac{4 \sqrt{15}}{5} \approx -3.098386677$$

Steps by Finding Square Root

Subtract 55 from 7 to get -48.

$$5x^{2}-48=0$$

Add 48 to both sides. Anything plus zero gives itself.

$$5x^{2}=48$$

Divide both sides by 5.

$$x^{2}=\frac{48}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{15}}{5} x=-\frac{4\sqrt{15}}{5}$$

Steps Using the Quadratic Formula

Subtract 55 from 7 to get -48.

$$5x^{2}-48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-48\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-48\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-48\right)}}{2\times 5}$$

Multiply -20 times -48.

$$x=\frac{0±\sqrt{960}}{2\times 5}$$

Take the square root of 960.

$$x=\frac{0±8\sqrt{15}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±8\sqrt{15}}{10}$$

Now solve the equation x=\frac{0±8\sqrt{15}}{10} when ± is plus.

$$x=\frac{4\sqrt{15}}{5}$$

Now solve the equation x=\frac{0±8\sqrt{15}}{10} when ± is minus.

$$x=-\frac{4\sqrt{15}}{5}$$

The equation is now solved.

$$x=\frac{4\sqrt{15}}{5} x=-\frac{4\sqrt{15}}{5}$$