Solve 9k^2/70+14k^2=1/2

$$\frac { 9 k ^ { 2 } } { 70 + 14 k ^ { 2 } } = \frac { 1 } { 2 }$$

Solve for k

$$k = \frac{\sqrt{70}}{2} \approx 4.183300133$$

$$k = -\frac{\sqrt{70}}{2} \approx -4.183300133$$

Steps by Finding Square Root

Multiply both sides of the equation by 14\left(k^{2}+5\right), the least common multiple of 70+14k^{2},2.

$$9k^{2}=7\left(k^{2}+5\right)$$

Use the distributive property to multiply 7 by k^{2}+5.

$$9k^{2}=7k^{2}+35$$

Subtract 7k^{2} from both sides.

$$9k^{2}-7k^{2}=35$$

Combine 9k^{2} and -7k^{2} to get 2k^{2}.

$$2k^{2}=35$$

Divide both sides by 2.

$$k^{2}=\frac{35}{2}$$

Take the square root of both sides of the equation.

$$k=\frac{\sqrt{70}}{2} k=-\frac{\sqrt{70}}{2}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 14\left(k^{2}+5\right), the least common multiple of 70+14k^{2},2.

$$9k^{2}=7\left(k^{2}+5\right)$$

Use the distributive property to multiply 7 by k^{2}+5.

$$9k^{2}=7k^{2}+35$$

Subtract 7k^{2} from both sides.

$$9k^{2}-7k^{2}=35$$

Combine 9k^{2} and -7k^{2} to get 2k^{2}.

$$2k^{2}=35$$

Subtract 35 from both sides.

$$2k^{2}-35=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -35 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\times 2\left(-35\right)}}{2\times 2}$$

Square 0.

$$k=\frac{0±\sqrt{-4\times 2\left(-35\right)}}{2\times 2}$$

Multiply -4 times 2.

$$k=\frac{0±\sqrt{-8\left(-35\right)}}{2\times 2}$$

Multiply -8 times -35.

$$k=\frac{0±\sqrt{280}}{2\times 2}$$

Take the square root of 280.

$$k=\frac{0±2\sqrt{70}}{2\times 2}$$

Multiply 2 times 2.

$$k=\frac{0±2\sqrt{70}}{4}$$

Now solve the equation k=\frac{0±2\sqrt{70}}{4} when ± is plus.

$$k=\frac{\sqrt{70}}{2}$$

Now solve the equation k=\frac{0±2\sqrt{70}}{4} when ± is minus.

$$k=-\frac{\sqrt{70}}{2}$$

The equation is now solved.

$$k=\frac{\sqrt{70}}{2} k=-\frac{\sqrt{70}}{2}$$