Solve 7x^2+5x^2=55

$$7 x ^ { 2 } + 5 x ^ { 2 } = 55$$

Solve for x

$$x = \frac{\sqrt{165}}{6} \approx 2.140872096$$

$$x = -\frac{\sqrt{165}}{6} \approx -2.140872096$$

Steps by Finding Square Root

Combine 7x^{2} and 5x^{2} to get 12x^{2}.

$$12x^{2}=55$$

Divide both sides by 12.

$$x^{2}=\frac{55}{12}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{165}}{6} x=-\frac{\sqrt{165}}{6}$$

Steps Using the Quadratic Formula

Combine 7x^{2} and 5x^{2} to get 12x^{2}.

$$12x^{2}=55$$

Subtract 55 from both sides.

$$12x^{2}-55=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, 0 for b, and -55 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 12\left(-55\right)}}{2\times 12}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 12\left(-55\right)}}{2\times 12}$$

Multiply -4 times 12.

$$x=\frac{0±\sqrt{-48\left(-55\right)}}{2\times 12}$$

Multiply -48 times -55.

$$x=\frac{0±\sqrt{2640}}{2\times 12}$$

Take the square root of 2640.

$$x=\frac{0±4\sqrt{165}}{2\times 12}$$

Multiply 2 times 12.

$$x=\frac{0±4\sqrt{165}}{24}$$

Now solve the equation x=\frac{0±4\sqrt{165}}{24} when ± is plus.

$$x=\frac{\sqrt{165}}{6}$$

Now solve the equation x=\frac{0±4\sqrt{165}}{24} when ± is minus.

$$x=-\frac{\sqrt{165}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{165}}{6} x=-\frac{\sqrt{165}}{6}$$