Solve 14(1-7x^2)/(7x^2+1)^2=0

$$\frac { 14 ( 1 - 7 x ^ { 2 } ) } { ( 7 x ^ { 2 } + 1 ) ^ { 2 } } = 0$$

Solve for x

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

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

Steps by Finding Square Root

Multiply both sides of the equation by \left(7x^{2}+1\right)^{2}.

$$14\left(1-7x^{2}\right)=0$$

Use the distributive property to multiply 14 by 1-7x^{2}.

$$14-98x^{2}=0$$

Subtract 14 from both sides. Anything subtracted from zero gives its negation.

$$-98x^{2}=-14$$

Divide both sides by -98.

$$x^{2}=\frac{-14}{-98}$$

Reduce the fraction \frac{-14}{-98} to lowest terms by extracting and canceling out -14.

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

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

Multiply both sides of the equation by \left(7x^{2}+1\right)^{2}.

$$14\left(1-7x^{2}\right)=0$$

Use the distributive property to multiply 14 by 1-7x^{2}.

$$14-98x^{2}=0$$

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.

$$-98x^{2}+14=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -98 for a, 0 for b, and 14 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-98\right)\times 14}}{2\left(-98\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-98\right)\times 14}}{2\left(-98\right)}$$

Multiply -4 times -98.

$$x=\frac{0±\sqrt{392\times 14}}{2\left(-98\right)}$$

Multiply 392 times 14.

$$x=\frac{0±\sqrt{5488}}{2\left(-98\right)}$$

Take the square root of 5488.

$$x=\frac{0±28\sqrt{7}}{2\left(-98\right)}$$

Multiply 2 times -98.

$$x=\frac{0±28\sqrt{7}}{-196}$$

Now solve the equation x=\frac{0±28\sqrt{7}}{-196} when ± is plus.

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

Now solve the equation x=\frac{0±28\sqrt{7}}{-196} when ± is minus.

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

The equation is now solved.

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