Solve x^2-3x^2+33=0

$$x ^ { 2 } - 3 x ^ { 2 } + 33 = 0$$

Solve for x

$$x = \frac{\sqrt{66}}{2} \approx 4.062019202$$

$$x = -\frac{\sqrt{66}}{2} \approx -4.062019202$$

Steps by Finding Square Root

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

$$-2x^{2}+33=0$$

Subtract 33 from both sides. Anything subtracted from zero gives its negation.

$$-2x^{2}=-33$$

Divide both sides by -2.

$$x^{2}=\frac{-33}{-2}$$

Fraction \frac{-33}{-2} can be simplified to \frac{33}{2} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{33}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{66}}{2} x=-\frac{\sqrt{66}}{2}$$

Steps Using the Quadratic Formula

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

$$-2x^{2}+33=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and 33 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 33}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\times 33}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\times 33}}{2\left(-2\right)}$$

Multiply 8 times 33.

$$x=\frac{0±\sqrt{264}}{2\left(-2\right)}$$

Take the square root of 264.

$$x=\frac{0±2\sqrt{66}}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±2\sqrt{66}}{-4}$$

Now solve the equation x=\frac{0±2\sqrt{66}}{-4} when ± is plus.

$$x=-\frac{\sqrt{66}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{66}}{-4} when ± is minus.

$$x=\frac{\sqrt{66}}{2}$$

The equation is now solved.

$$x=-\frac{\sqrt{66}}{2} x=\frac{\sqrt{66}}{2}$$