Solve x*7x=12

$$x \times 7x=12$$

Solve for x

$$x = \frac{2 \sqrt{21}}{7} \approx 1.309307341$$

$$x = -\frac{2 \sqrt{21}}{7} \approx -1.309307341$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$x^{2}\times 7=12$$

Divide both sides by 7.

$$x^{2}=\frac{12}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{21}}{7} x=-\frac{2\sqrt{21}}{7}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$x^{2}\times 7=12$$

Subtract 12 from both sides.

$$x^{2}\times 7-12=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$7x^{2}-12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\left(-12\right)}}{2\times 7}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7\left(-12\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\left(-12\right)}}{2\times 7}$$

Multiply -28 times -12.

$$x=\frac{0±\sqrt{336}}{2\times 7}$$

Take the square root of 336.

$$x=\frac{0±4\sqrt{21}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±4\sqrt{21}}{14}$$

Now solve the equation x=\frac{0±4\sqrt{21}}{14} when ± is plus.

$$x=\frac{2\sqrt{21}}{7}$$

Now solve the equation x=\frac{0±4\sqrt{21}}{14} when ± is minus.

$$x=-\frac{2\sqrt{21}}{7}$$

The equation is now solved.

$$x=\frac{2\sqrt{21}}{7} x=-\frac{2\sqrt{21}}{7}$$