Solve left(-7*xright)^2-14-14=0

$${ \left(-7 \times x \right) }^{ 2 } -14-14=0$$

Solve for x

$$x=-\frac{2\sqrt{7}}{7}\approx -0.755928946$$

$$x=\frac{2\sqrt{7}}{7}\approx 0.755928946$$

Steps by Finding Square Root

Expand \left(-7x\right)^{2}.

$$\left(-7\right)^{2}x^{2}-14-14=0$$

Calculate -7 to the power of 2 and get 49.

$$49x^{2}-14-14=0$$

Subtract 14 from -14 to get -28.

$$49x^{2}-28=0$$

Add 28 to both sides. Anything plus zero gives itself.

$$49x^{2}=28$$

Divide both sides by 49.

$$x^{2}=\frac{28}{49}$$

Reduce the fraction \frac{28}{49} to lowest terms by extracting and canceling out 7.

$$x^{2}=\frac{4}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{7}}{7} x=-\frac{2\sqrt{7}}{7}$$

Steps Using the Quadratic Formula

Expand \left(-7x\right)^{2}.

$$\left(-7\right)^{2}x^{2}-14-14=0$$

Calculate -7 to the power of 2 and get 49.

$$49x^{2}-14-14=0$$

Subtract 14 from -14 to get -28.

$$49x^{2}-28=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 49 for a, 0 for b, and -28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 49\left(-28\right)}}{2\times 49}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 49\left(-28\right)}}{2\times 49}$$

Multiply -4 times 49.

$$x=\frac{0±\sqrt{-196\left(-28\right)}}{2\times 49}$$

Multiply -196 times -28.

$$x=\frac{0±\sqrt{5488}}{2\times 49}$$

Take the square root of 5488.

$$x=\frac{0±28\sqrt{7}}{2\times 49}$$

Multiply 2 times 49.

$$x=\frac{0±28\sqrt{7}}{98}$$

Now solve the equation x=\frac{0±28\sqrt{7}}{98} when ± is plus.

$$x=\frac{2\sqrt{7}}{7}$$

Now solve the equation x=\frac{0±28\sqrt{7}}{98} when ± is minus.

$$x=-\frac{2\sqrt{7}}{7}$$

The equation is now solved.

$$x=\frac{2\sqrt{7}}{7} x=-\frac{2\sqrt{7}}{7}$$