Solve 4x^2-x^2=4

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

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

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

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

Divide both sides by 3.

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

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

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

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

Subtract 4 from both sides.

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

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}.

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

Square 0.

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

Multiply -4 times 3.

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

Multiply -12 times -4.

$$x=\frac{0±\sqrt{48}}{2\times 3}$$

Take the square root of 48.

$$x=\frac{0±4\sqrt{3}}{2\times 3}$$

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.

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