Solve 3x^2+4x^2=100

$$3 { x }^{ 2 } +4 { x }^{ 2 } =100$$

Solve for x

$$x = \frac{10 \sqrt{7}}{7} \approx 3.77964473$$

$$x = -\frac{10 \sqrt{7}}{7} \approx -3.77964473$$

Steps by Finding Square Root

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

$$7x^{2}=100$$

Divide both sides by 7.

$$x^{2}=\frac{100}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{10\sqrt{7}}{7} x=-\frac{10\sqrt{7}}{7}$$

Steps Using the Quadratic Formula

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

$$7x^{2}=100$$

Subtract 100 from both sides.

$$7x^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\left(-100\right)}}{2\times 7}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7\left(-100\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\left(-100\right)}}{2\times 7}$$

Multiply -28 times -100.

$$x=\frac{0±\sqrt{2800}}{2\times 7}$$

Take the square root of 2800.

$$x=\frac{0±20\sqrt{7}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±20\sqrt{7}}{14}$$

Now solve the equation x=\frac{0±20\sqrt{7}}{14} when ± is plus.

$$x=\frac{10\sqrt{7}}{7}$$

Now solve the equation x=\frac{0±20\sqrt{7}}{14} when ± is minus.

$$x=-\frac{10\sqrt{7}}{7}$$

The equation is now solved.

$$x=\frac{10\sqrt{7}}{7} x=-\frac{10\sqrt{7}}{7}$$