Solve -9/324x^2+9=-7

$$- \frac { 9 } { 324 } x ^ { 2 } + 9 = - 7$$

Solve for x

$$x=24$$

$$x=-24$$

Steps by Finding Square Root

Reduce the fraction \frac{9}{324} to lowest terms by extracting and canceling out 9.

$$-\frac{1}{36}x^{2}+9=-7$$

Subtract 9 from both sides.

$$-\frac{1}{36}x^{2}=-7-9$$

Subtract 9 from -7 to get -16.

$$-\frac{1}{36}x^{2}=-16$$

Multiply both sides by -36, the reciprocal of -\frac{1}{36}.

$$x^{2}=-16\left(-36\right)$$

Multiply -16 and -36 to get 576.

$$x^{2}=576$$

Take the square root of both sides of the equation.

$$x=24 x=-24$$

Steps Using the Quadratic Formula

Reduce the fraction \frac{9}{324} to lowest terms by extracting and canceling out 9.

$$-\frac{1}{36}x^{2}+9=-7$$

Add 7 to both sides.

$$-\frac{1}{36}x^{2}+9+7=0$$

Add 9 and 7 to get 16.

$$-\frac{1}{36}x^{2}+16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{1}{36} for a, 0 for b, and 16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{36}\right)\times 16}}{2\left(-\frac{1}{36}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{36}\right)\times 16}}{2\left(-\frac{1}{36}\right)}$$

Multiply -4 times -\frac{1}{36}.

$$x=\frac{0±\sqrt{\frac{1}{9}\times 16}}{2\left(-\frac{1}{36}\right)}$$

Multiply \frac{1}{9} times 16.

$$x=\frac{0±\sqrt{\frac{16}{9}}}{2\left(-\frac{1}{36}\right)}$$

Take the square root of \frac{16}{9}.

$$x=\frac{0±\frac{4}{3}}{2\left(-\frac{1}{36}\right)}$$

Multiply 2 times -\frac{1}{36}.

$$x=\frac{0±\frac{4}{3}}{-\frac{1}{18}}$$

Now solve the equation x=\frac{0±\frac{4}{3}}{-\frac{1}{18}} when ± is plus.

$$x=-24$$

Now solve the equation x=\frac{0±\frac{4}{3}}{-\frac{1}{18}} when ± is minus.

$$x=24$$

The equation is now solved.

$$x=-24 x=24$$