Solve 7-49x^2=0

$$7-49 { x }^{ 2 } =0$$

Solve for x

$$x=\frac{\sqrt{7}}{7}\approx 0.377964473$$

$$x=-\frac{\sqrt{7}}{7}\approx -0.377964473$$

Steps by Finding Square Root

Subtract 7 from both sides. Anything subtracted from zero gives its negation.

$$-49x^{2}=-7$$

Divide both sides by -49.

$$x^{2}=\frac{-7}{-49}$$

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

$$x^{2}=\frac{1}{7}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-49x^{2}+7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -49 for a, 0 for b, and 7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-49\right)\times 7}}{2\left(-49\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-49\right)\times 7}}{2\left(-49\right)}$$

Multiply -4 times -49.

$$x=\frac{0±\sqrt{196\times 7}}{2\left(-49\right)}$$

Multiply 196 times 7.

$$x=\frac{0±\sqrt{1372}}{2\left(-49\right)}$$

Take the square root of 1372.

$$x=\frac{0±14\sqrt{7}}{2\left(-49\right)}$$

Multiply 2 times -49.

$$x=\frac{0±14\sqrt{7}}{-98}$$

Now solve the equation x=\frac{0±14\sqrt{7}}{-98} when ± is plus.

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

Now solve the equation x=\frac{0±14\sqrt{7}}{-98} when ± is minus.

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

The equation is now solved.

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