Solve 7x^2+3=7

$$7 x ^ { 2 } + 3 = 7$$

Solve for x

$$x=\frac{2\sqrt{7}}{7}\approx 0.755928946$$

$$x=-\frac{2\sqrt{7}}{7}\approx -0.755928946$$

Steps by Finding Square Root

Subtract 3 from both sides.

$$7x^{2}=7-3$$

Subtract 3 from 7 to get 4.

$$7x^{2}=4$$

Divide both sides by 7.

$$x^{2}=\frac{4}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{7}}{7} x=-\frac{2\sqrt{7}}{7}$$

Steps Using the Quadratic Formula

Subtract 7 from both sides.

$$7x^{2}+3-7=0$$

Subtract 7 from 3 to get -4.

$$7x^{2}-4=0$$

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

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

Square 0.

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

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\left(-4\right)}}{2\times 7}$$

Multiply -28 times -4.

$$x=\frac{0±\sqrt{112}}{2\times 7}$$

Take the square root of 112.

$$x=\frac{0±4\sqrt{7}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±4\sqrt{7}}{14}$$

Now solve the equation x=\frac{0±4\sqrt{7}}{14} when ± is plus.

$$x=\frac{2\sqrt{7}}{7}$$

Now solve the equation x=\frac{0±4\sqrt{7}}{14} when ± is minus.

$$x=-\frac{2\sqrt{7}}{7}$$

The equation is now solved.

$$x=\frac{2\sqrt{7}}{7} x=-\frac{2\sqrt{7}}{7}$$