Solve 5x^2+2x^2=1

$$5 x ^ { 2 } + 2 x ^ { 2 } = 1$$

Solve for x

$$x=\frac{\sqrt{7}}{7}\approx 0.377964473$$

$$x=-\frac{\sqrt{7}}{7}\approx -0.377964473$$

Steps by Finding Square Root

Combine 5x^{2} and 2x^{2} to get 7x^{2}.

$$7x^{2}=1$$

Divide both sides by 7.

$$x^{2}=\frac{1}{7}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Combine 5x^{2} and 2x^{2} to get 7x^{2}.

$$7x^{2}=1$$

Subtract 1 from both sides.

$$7x^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\left(-1\right)}}{2\times 7}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7\left(-1\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\left(-1\right)}}{2\times 7}$$

Multiply -28 times -1.

$$x=\frac{0±\sqrt{28}}{2\times 7}$$

Take the square root of 28.

$$x=\frac{0±2\sqrt{7}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±2\sqrt{7}}{14}$$

Now solve the equation x=\frac{0±2\sqrt{7}}{14} when ± is plus.

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

Now solve the equation x=\frac{0±2\sqrt{7}}{14} when ± is minus.

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

The equation is now solved.

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