Solve 5x^2+1div2(x^2-60)=0

$$5 { x }^{ 2 } +1 \div 2( { x }^{ 2 } -60)=0$$

Solve for x

$$x = \frac{2 \sqrt{165}}{11} \approx 2.335496832$$

$$x = -\frac{2 \sqrt{165}}{11} \approx -2.335496832$$

Steps by Finding Square Root

Use the distributive property to multiply \frac{1}{2} by x^{2}-60.

$$5x^{2}+\frac{1}{2}x^{2}-30=0$$

Combine 5x^{2} and \frac{1}{2}x^{2} to get \frac{11}{2}x^{2}.

$$\frac{11}{2}x^{2}-30=0$$

Add 30 to both sides. Anything plus zero gives itself.

$$\frac{11}{2}x^{2}=30$$

Multiply both sides by \frac{2}{11}, the reciprocal of \frac{11}{2}.

$$x^{2}=30\times \frac{2}{11}$$

Multiply 30 and \frac{2}{11} to get \frac{60}{11}.

$$x^{2}=\frac{60}{11}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{165}}{11} x=-\frac{2\sqrt{165}}{11}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply \frac{1}{2} by x^{2}-60.

$$5x^{2}+\frac{1}{2}x^{2}-30=0$$

Combine 5x^{2} and \frac{1}{2}x^{2} to get \frac{11}{2}x^{2}.

$$\frac{11}{2}x^{2}-30=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{11}{2} for a, 0 for b, and -30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{11}{2}\left(-30\right)}}{2\times \frac{11}{2}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{11}{2}\left(-30\right)}}{2\times \frac{11}{2}}$$

Multiply -4 times \frac{11}{2}.

$$x=\frac{0±\sqrt{-22\left(-30\right)}}{2\times \frac{11}{2}}$$

Multiply -22 times -30.

$$x=\frac{0±\sqrt{660}}{2\times \frac{11}{2}}$$

Take the square root of 660.

$$x=\frac{0±2\sqrt{165}}{2\times \frac{11}{2}}$$

Multiply 2 times \frac{11}{2}.

$$x=\frac{0±2\sqrt{165}}{11}$$

Now solve the equation x=\frac{0±2\sqrt{165}}{11} when ± is plus.

$$x=\frac{2\sqrt{165}}{11}$$

Now solve the equation x=\frac{0±2\sqrt{165}}{11} when ± is minus.

$$x=-\frac{2\sqrt{165}}{11}$$

The equation is now solved.

$$x=\frac{2\sqrt{165}}{11} x=-\frac{2\sqrt{165}}{11}$$