Solve 2x^2+9x^2=2000

$$2 x ^ { 2 } + 9 x ^ { 2 } = 2000$$

Solve for x

$$x = \frac{20 \sqrt{55}}{11} \approx 13.483997249$$

$$x = -\frac{20 \sqrt{55}}{11} \approx -13.483997249$$

Steps by Finding Square Root

Combine 2x^{2} and 9x^{2} to get 11x^{2}.

$$11x^{2}=2000$$

Divide both sides by 11.

$$x^{2}=\frac{2000}{11}$$

Take the square root of both sides of the equation.

$$x=\frac{20\sqrt{55}}{11} x=-\frac{20\sqrt{55}}{11}$$

Steps Using the Quadratic Formula

Combine 2x^{2} and 9x^{2} to get 11x^{2}.

$$11x^{2}=2000$$

Subtract 2000 from both sides.

$$11x^{2}-2000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 11 for a, 0 for b, and -2000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 11\left(-2000\right)}}{2\times 11}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 11\left(-2000\right)}}{2\times 11}$$

Multiply -4 times 11.

$$x=\frac{0±\sqrt{-44\left(-2000\right)}}{2\times 11}$$

Multiply -44 times -2000.

$$x=\frac{0±\sqrt{88000}}{2\times 11}$$

Take the square root of 88000.

$$x=\frac{0±40\sqrt{55}}{2\times 11}$$

Multiply 2 times 11.

$$x=\frac{0±40\sqrt{55}}{22}$$

Now solve the equation x=\frac{0±40\sqrt{55}}{22} when ± is plus.

$$x=\frac{20\sqrt{55}}{11}$$

Now solve the equation x=\frac{0±40\sqrt{55}}{22} when ± is minus.

$$x=-\frac{20\sqrt{55}}{11}$$

The equation is now solved.

$$x=\frac{20\sqrt{55}}{11} x=-\frac{20\sqrt{55}}{11}$$