Solve (y+4)*y=96

$$( y + 4 ) \cdot y = 96$$

Solve for y

$$y=-12$$

$$y=8$$

Steps Using the Quadratic Formula

Use the distributive property to multiply y+4 by y.

$$y^{2}+4y=96$$

Subtract 96 from both sides.

$$y^{2}+4y-96=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 4 for b, and -96 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-4±\sqrt{4^{2}-4\left(-96\right)}}{2}$$

Square 4.

$$y=\frac{-4±\sqrt{16-4\left(-96\right)}}{2}$$

Multiply -4 times -96.

$$y=\frac{-4±\sqrt{16+384}}{2}$$

Add 16 to 384.

$$y=\frac{-4±\sqrt{400}}{2}$$

Take the square root of 400.

$$y=\frac{-4±20}{2}$$

Now solve the equation y=\frac{-4±20}{2} when ± is plus. Add -4 to 20.

$$y=\frac{16}{2}$$

Divide 16 by 2.

$$y=8$$

Now solve the equation y=\frac{-4±20}{2} when ± is minus. Subtract 20 from -4.

$$y=-\frac{24}{2}$$

Divide -24 by 2.

$$y=-12$$

The equation is now solved.

$$y=8 y=-12$$

Steps for Completing the Square

Use the distributive property to multiply y+4 by y.

$$y^{2}+4y=96$$

Divide 4, the coefficient of the x term, by 2 to get 2. Then add the square of 2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$y^{2}+4y+2^{2}=96+2^{2}$$

Square 2.

$$y^{2}+4y+4=96+4$$

Add 96 to 4.

$$y^{2}+4y+4=100$$

Factor y^{2}+4y+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(y+2\right)^{2}=100$$

Take the square root of both sides of the equation.

$$\sqrt{\left(y+2\right)^{2}}=\sqrt{100}$$

Simplify.

$$y+2=10 y+2=-10$$

Subtract 2 from both sides of the equation.

$$y=8 y=-12$$