Solve 14/x^2+1=5

$$\frac { 14 } { x ^ { 2 } + 1 } = 5$$

Solve for x

$$x = \frac{3 \sqrt{5}}{5} \approx 1.341640786$$

$$x = -\frac{3 \sqrt{5}}{5} \approx -1.341640786$$

Steps by Finding Square Root

Multiply both sides of the equation by x^{2}+1.

$$14=5\left(x^{2}+1\right)$$

Use the distributive property to multiply 5 by x^{2}+1.

$$14=5x^{2}+5$$

Swap sides so that all variable terms are on the left hand side.

$$5x^{2}+5=14$$

Subtract 5 from both sides.

$$5x^{2}=14-5$$

Subtract 5 from 14 to get 9.

$$5x^{2}=9$$

Divide both sides by 5.

$$x^{2}=\frac{9}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{5}}{5} x=-\frac{3\sqrt{5}}{5}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by x^{2}+1.

$$14=5\left(x^{2}+1\right)$$

Use the distributive property to multiply 5 by x^{2}+1.

$$14=5x^{2}+5$$

Swap sides so that all variable terms are on the left hand side.

$$5x^{2}+5=14$$

Subtract 14 from both sides.

$$5x^{2}+5-14=0$$

Subtract 14 from 5 to get -9.

$$5x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-9\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-9\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-9\right)}}{2\times 5}$$

Multiply -20 times -9.

$$x=\frac{0±\sqrt{180}}{2\times 5}$$

Take the square root of 180.

$$x=\frac{0±6\sqrt{5}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±6\sqrt{5}}{10}$$

Now solve the equation x=\frac{0±6\sqrt{5}}{10} when ± is plus.

$$x=\frac{3\sqrt{5}}{5}$$

Now solve the equation x=\frac{0±6\sqrt{5}}{10} when ± is minus.

$$x=-\frac{3\sqrt{5}}{5}$$

The equation is now solved.

$$x=\frac{3\sqrt{5}}{5} x=-\frac{3\sqrt{5}}{5}$$