Solve -6(y+7)^2=-294

$$- 6 ( y + 7 ) ^ { 2 } = - 294$$

Solve for y

$$y=0$$

$$y=-14$$

Steps Using Factoring

Divide both sides by -6.

$$\left(y+7\right)^{2}=\frac{-294}{-6}$$

Divide -294 by -6 to get 49.

$$\left(y+7\right)^{2}=49$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+7\right)^{2}.

$$y^{2}+14y+49=49$$

Subtract 49 from both sides.

$$y^{2}+14y+49-49=0$$

Subtract 49 from 49 to get 0.

$$y^{2}+14y=0$$

Factor out y.

$$y\left(y+14\right)=0$$

To find equation solutions, solve y=0 and y+14=0.

$$y=0 y=-14$$

Steps Using the Quadratic Formula

Divide both sides by -6.

$$\left(y+7\right)^{2}=\frac{-294}{-6}$$

Divide -294 by -6 to get 49.

$$\left(y+7\right)^{2}=49$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+7\right)^{2}.

$$y^{2}+14y+49=49$$

Subtract 49 from both sides.

$$y^{2}+14y+49-49=0$$

Subtract 49 from 49 to get 0.

$$y^{2}+14y=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 14 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-14±\sqrt{14^{2}}}{2}$$

Take the square root of 14^{2}.

$$y=\frac{-14±14}{2}$$

Now solve the equation y=\frac{-14±14}{2} when ± is plus. Add -14 to 14.

$$y=\frac{0}{2}$$

Divide 0 by 2.

$$y=0$$

Now solve the equation y=\frac{-14±14}{2} when ± is minus. Subtract 14 from -14.

$$y=-\frac{28}{2}$$

Divide -28 by 2.

$$y=-14$$

The equation is now solved.

$$y=0 y=-14$$

Steps for Completing the Square

Divide both sides by -6.

$$\left(y+7\right)^{2}=\frac{-294}{-6}$$

Divide -294 by -6 to get 49.

$$\left(y+7\right)^{2}=49$$

Take the square root of both sides of the equation.

$$\sqrt{\left(y+7\right)^{2}}=\sqrt{49}$$

Simplify.

$$y+7=7 y+7=-7$$

Subtract 7 from both sides of the equation.

$$y=0 y=-14$$