Solve 2x^2+x^2+15=240

$$2 x ^ { 2 } + x ^ { 2 } + 15 = 240$$

Solve for x

$$x=5\sqrt{3}\approx 8.660254038$$

$$x=-5\sqrt{3}\approx -8.660254038$$

Steps by Finding Square Root

Combine 2x^{2} and x^{2} to get 3x^{2}.

$$3x^{2}+15=240$$

Subtract 15 from both sides.

$$3x^{2}=240-15$$

Subtract 15 from 240 to get 225.

$$3x^{2}=225$$

Divide both sides by 3.

$$x^{2}=\frac{225}{3}$$

Divide 225 by 3 to get 75.

$$x^{2}=75$$

Take the square root of both sides of the equation.

$$x=5\sqrt{3} x=-5\sqrt{3}$$

Steps Using the Quadratic Formula

Combine 2x^{2} and x^{2} to get 3x^{2}.

$$3x^{2}+15=240$$

Subtract 240 from both sides.

$$3x^{2}+15-240=0$$

Subtract 240 from 15 to get -225.

$$3x^{2}-225=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -225 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-225\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-225\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-225\right)}}{2\times 3}$$

Multiply -12 times -225.

$$x=\frac{0±\sqrt{2700}}{2\times 3}$$

Take the square root of 2700.

$$x=\frac{0±30\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±30\sqrt{3}}{6}$$

Now solve the equation x=\frac{0±30\sqrt{3}}{6} when ± is plus.

$$x=5\sqrt{3}$$

Now solve the equation x=\frac{0±30\sqrt{3}}{6} when ± is minus.

$$x=-5\sqrt{3}$$

The equation is now solved.

$$x=5\sqrt{3} x=-5\sqrt{3}$$