Solve 3x^2+4x^2=20^2

$$3 x ^ { 2 } + 4 x ^ { 2 } = 20 ^ { 2 }$$

Solve for x

$$x = \frac{20 \sqrt{7}}{7} \approx 7.55928946$$

$$x = -\frac{20 \sqrt{7}}{7} \approx -7.55928946$$

Steps by Finding Square Root

Combine 3x^{2} and 4x^{2} to get 7x^{2}.

$$7x^{2}=20^{2}$$

Calculate 20 to the power of 2 and get 400.

$$7x^{2}=400$$

Divide both sides by 7.

$$x^{2}=\frac{400}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{20\sqrt{7}}{7} x=-\frac{20\sqrt{7}}{7}$$

Steps Using the Quadratic Formula

Combine 3x^{2} and 4x^{2} to get 7x^{2}.

$$7x^{2}=20^{2}$$

Calculate 20 to the power of 2 and get 400.

$$7x^{2}=400$$

Subtract 400 from both sides.

$$7x^{2}-400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and -400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\left(-400\right)}}{2\times 7}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7\left(-400\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\left(-400\right)}}{2\times 7}$$

Multiply -28 times -400.

$$x=\frac{0±\sqrt{11200}}{2\times 7}$$

Take the square root of 11200.

$$x=\frac{0±40\sqrt{7}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±40\sqrt{7}}{14}$$

Now solve the equation x=\frac{0±40\sqrt{7}}{14} when ± is plus.

$$x=\frac{20\sqrt{7}}{7}$$

Now solve the equation x=\frac{0±40\sqrt{7}}{14} when ± is minus.

$$x=-\frac{20\sqrt{7}}{7}$$

The equation is now solved.

$$x=\frac{20\sqrt{7}}{7} x=-\frac{20\sqrt{7}}{7}$$