Solve -9-7k^2=-576

$$- 9 - 7 k ^ { 2 } = - 576$$

Solve for k

$$k=9$$

$$k=-9$$

Steps by Finding Square Root

Add 9 to both sides.

$$-7k^{2}=-576+9$$

Add -576 and 9 to get -567.

$$-7k^{2}=-567$$

Divide both sides by -7.

$$k^{2}=\frac{-567}{-7}$$

Divide -567 by -7 to get 81.

$$k^{2}=81$$

Take the square root of both sides of the equation.

$$k=9 k=-9$$

Steps Using the Quadratic Formula

Add 576 to both sides.

$$-9-7k^{2}+576=0$$

Add -9 and 576 to get 567.

$$567-7k^{2}=0$$

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.

$$-7k^{2}+567=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -7 for a, 0 for b, and 567 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\left(-7\right)\times 567}}{2\left(-7\right)}$$

Square 0.

$$k=\frac{0±\sqrt{-4\left(-7\right)\times 567}}{2\left(-7\right)}$$

Multiply -4 times -7.

$$k=\frac{0±\sqrt{28\times 567}}{2\left(-7\right)}$$

Multiply 28 times 567.

$$k=\frac{0±\sqrt{15876}}{2\left(-7\right)}$$

Take the square root of 15876.

$$k=\frac{0±126}{2\left(-7\right)}$$

Multiply 2 times -7.

$$k=\frac{0±126}{-14}$$

Now solve the equation k=\frac{0±126}{-14} when ± is plus. Divide 126 by -14.

$$k=-9$$

Now solve the equation k=\frac{0±126}{-14} when ± is minus. Divide -126 by -14.

$$k=9$$

The equation is now solved.

$$k=-9 k=9$$