Solve 18x^2-36-78+32x^2=25

$$18 { x }^{ 2 } -36-78+32 { x }^{ 2 } =25$$

Solve for x

$$x = \frac{\sqrt{278}}{10} \approx 1.6673332$$

$$x = -\frac{\sqrt{278}}{10} \approx -1.6673332$$

Steps by Finding Square Root

Subtract 78 from -36 to get -114.

$$18x^{2}-114+32x^{2}=25$$

Combine 18x^{2} and 32x^{2} to get 50x^{2}.

$$50x^{2}-114=25$$

Add 114 to both sides.

$$50x^{2}=25+114$$

Add 25 and 114 to get 139.

$$50x^{2}=139$$

Divide both sides by 50.

$$x^{2}=\frac{139}{50}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{278}}{10} x=-\frac{\sqrt{278}}{10}$$

Steps Using the Quadratic Formula

Subtract 78 from -36 to get -114.

$$18x^{2}-114+32x^{2}=25$$

Combine 18x^{2} and 32x^{2} to get 50x^{2}.

$$50x^{2}-114=25$$

Subtract 25 from both sides.

$$50x^{2}-114-25=0$$

Subtract 25 from -114 to get -139.

$$50x^{2}-139=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 50 for a, 0 for b, and -139 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 50\left(-139\right)}}{2\times 50}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 50\left(-139\right)}}{2\times 50}$$

Multiply -4 times 50.

$$x=\frac{0±\sqrt{-200\left(-139\right)}}{2\times 50}$$

Multiply -200 times -139.

$$x=\frac{0±\sqrt{27800}}{2\times 50}$$

Take the square root of 27800.

$$x=\frac{0±10\sqrt{278}}{2\times 50}$$

Multiply 2 times 50.

$$x=\frac{0±10\sqrt{278}}{100}$$

Now solve the equation x=\frac{0±10\sqrt{278}}{100} when ± is plus.

$$x=\frac{\sqrt{278}}{10}$$

Now solve the equation x=\frac{0±10\sqrt{278}}{100} when ± is minus.

$$x=-\frac{\sqrt{278}}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{278}}{10} x=-\frac{\sqrt{278}}{10}$$