Solve 5x^2+88x^2-240=0

$$5 { x }^{ 2 } +88 { x }^{ 2 } -240 = 0$$

Solve for x

$$x = \frac{4 \sqrt{155}}{31} \approx 1.606438658$$

$$x = -\frac{4 \sqrt{155}}{31} \approx -1.606438658$$

Steps by Finding Square Root

Combine 5x^{2} and 88x^{2} to get 93x^{2}.

$$93x^{2}-240=0$$

Add 240 to both sides. Anything plus zero gives itself.

$$93x^{2}=240$$

Divide both sides by 93.

$$x^{2}=\frac{240}{93}$$

Reduce the fraction \frac{240}{93} to lowest terms by extracting and canceling out 3.

$$x^{2}=\frac{80}{31}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{155}}{31} x=-\frac{4\sqrt{155}}{31}$$

Steps Using the Quadratic Formula

Combine 5x^{2} and 88x^{2} to get 93x^{2}.

$$93x^{2}-240=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 93 for a, 0 for b, and -240 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 93\left(-240\right)}}{2\times 93}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 93\left(-240\right)}}{2\times 93}$$

Multiply -4 times 93.

$$x=\frac{0±\sqrt{-372\left(-240\right)}}{2\times 93}$$

Multiply -372 times -240.

$$x=\frac{0±\sqrt{89280}}{2\times 93}$$

Take the square root of 89280.

$$x=\frac{0±24\sqrt{155}}{2\times 93}$$

Multiply 2 times 93.

$$x=\frac{0±24\sqrt{155}}{186}$$

Now solve the equation x=\frac{0±24\sqrt{155}}{186} when ± is plus.

$$x=\frac{4\sqrt{155}}{31}$$

Now solve the equation x=\frac{0±24\sqrt{155}}{186} when ± is minus.

$$x=-\frac{4\sqrt{155}}{31}$$

The equation is now solved.

$$x=\frac{4\sqrt{155}}{31} x=-\frac{4\sqrt{155}}{31}$$