Solve x^2+21=4x^2+17

$$x ^ { 2 } + 21 = 4 x ^ { 2 } + 17$$

Solve for x

$$x = \frac{2 \sqrt{3}}{3} \approx 1.154700538$$

$$x = -\frac{2 \sqrt{3}}{3} \approx -1.154700538$$

Steps by Finding Square Root

Subtract 4x^{2} from both sides.

$$x^{2}+21-4x^{2}=17$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}+21=17$$

Subtract 21 from both sides.

$$-3x^{2}=17-21$$

Subtract 21 from 17 to get -4.

$$-3x^{2}=-4$$

Divide both sides by -3.

$$x^{2}=\frac{-4}{-3}$$

Fraction \frac{-4}{-3} can be simplified to \frac{4}{3} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{4}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{3}}{3} x=-\frac{2\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

Subtract 4x^{2} from both sides.

$$x^{2}+21-4x^{2}=17$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}+21=17$$

Subtract 17 from both sides.

$$-3x^{2}+21-17=0$$

Subtract 17 from 21 to get 4.

$$-3x^{2}+4=0$$

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

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

Square 0.

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

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\times 4}}{2\left(-3\right)}$$

Multiply 12 times 4.

$$x=\frac{0±\sqrt{48}}{2\left(-3\right)}$$

Take the square root of 48.

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

Multiply 2 times -3.

$$x=\frac{0±4\sqrt{3}}{-6}$$

Now solve the equation x=\frac{0±4\sqrt{3}}{-6} when ± is plus.

$$x=-\frac{2\sqrt{3}}{3}$$

Now solve the equation x=\frac{0±4\sqrt{3}}{-6} when ± is minus.

$$x=\frac{2\sqrt{3}}{3}$$

The equation is now solved.

$$x=-\frac{2\sqrt{3}}{3} x=\frac{2\sqrt{3}}{3}$$