Solve 7/36*x^2-1=0

$$\frac { 7 } { 36 } \cdot x ^ { 2 } - 1 = 0$$

Solve for x

$$x = \frac{6 \sqrt{7}}{7} \approx 2.267786838$$

$$x = -\frac{6 \sqrt{7}}{7} \approx -2.267786838$$

Steps by Finding Square Root

Add 1 to both sides. Anything plus zero gives itself.

$$\frac{7}{36}x^{2}=1$$

Multiply both sides by \frac{36}{7}, the reciprocal of \frac{7}{36}.

$$x^{2}=1\times \frac{36}{7}$$

Multiply 1 and \frac{36}{7} to get \frac{36}{7}.

$$x^{2}=\frac{36}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{6\sqrt{7}}{7} x=-\frac{6\sqrt{7}}{7}$$

Steps Using the Quadratic Formula

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.

$$\frac{7}{36}x^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{7}{36} for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{7}{36}\left(-1\right)}}{2\times \frac{7}{36}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{7}{36}\left(-1\right)}}{2\times \frac{7}{36}}$$

Multiply -4 times \frac{7}{36}.

$$x=\frac{0±\sqrt{-\frac{7}{9}\left(-1\right)}}{2\times \frac{7}{36}}$$

Multiply -\frac{7}{9} times -1.

$$x=\frac{0±\sqrt{\frac{7}{9}}}{2\times \frac{7}{36}}$$

Take the square root of \frac{7}{9}.

$$x=\frac{0±\frac{\sqrt{7}}{3}}{2\times \frac{7}{36}}$$

Multiply 2 times \frac{7}{36}.

$$x=\frac{0±\frac{\sqrt{7}}{3}}{\frac{7}{18}}$$

Now solve the equation x=\frac{0±\frac{\sqrt{7}}{3}}{\frac{7}{18}} when ± is plus.

$$x=\frac{6\sqrt{7}}{7}$$

Now solve the equation x=\frac{0±\frac{\sqrt{7}}{3}}{\frac{7}{18}} when ± is minus.

$$x=-\frac{6\sqrt{7}}{7}$$

The equation is now solved.

$$x=\frac{6\sqrt{7}}{7} x=-\frac{6\sqrt{7}}{7}$$