Solve x^2+3x^2=16*3

$${ x }^{ 2 } +3 { x }^{ 2 } =16 \times 3$$

Solve for x

$$x=2\sqrt{3}\approx 3.464101615$$

$$x=-2\sqrt{3}\approx -3.464101615$$

Steps by Finding Square Root

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

$$4x^{2}=16\times 3$$

Multiply 16 and 3 to get 48.

$$4x^{2}=48$$

Divide both sides by 4.

$$x^{2}=\frac{48}{4}$$

Divide 48 by 4 to get 12.

$$x^{2}=12$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

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

$$4x^{2}=16\times 3$$

Multiply 16 and 3 to get 48.

$$4x^{2}=48$$

Subtract 48 from both sides.

$$4x^{2}-48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-48\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-48\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-48\right)}}{2\times 4}$$

Multiply -16 times -48.

$$x=\frac{0±\sqrt{768}}{2\times 4}$$

Take the square root of 768.

$$x=\frac{0±16\sqrt{3}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±16\sqrt{3}}{8}$$

Now solve the equation x=\frac{0±16\sqrt{3}}{8} when ± is plus.

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

Now solve the equation x=\frac{0±16\sqrt{3}}{8} when ± is minus.

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

The equation is now solved.

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