Chapter 9, Problem 33SGR

To determine

To solve the given equation by factoring.

Answer to Problem 33SGR

The value of y is -4 and 8 .

Explanation of Solution

Given information :

The equation provided is $y^2-4y=32$ . This can be written as $y^2-4y-32=0$ .

Formula used :

The given equation can be solved by factoring. To do so, break up the midpoint to arrive at two factors. Then use the zero-product property to equate each factor in order to get the roots.

Calculation :

  $y^2-4y-32=0$

Equation to be solved.

  $=>y^2-8x+4x-32=0$

Breaking the middle term that when multiplied, provides that values of $a{x}^2\times c$ .

  $=>y\left(y-8\right)+4\left(y-8\right)=0$

Arranging the common factors.

  $=>\left(y+4\right)\left(y-8\right)=0$

The two factors of the function.

Now, the first root is:

  $y+4=0$

Using zero-product property.

  $y=-4$

The second root is:

  $y-8=0$

Using zero-product property.

  $y=8$

Thus, the values of y are is -4 and 8 .

To check the solutions, put them in the given equation and verify that left-hand and right-hand sides are equal.

For $y=-4$

  ${\left(-4\right)}^2-4\left(-4\right)-32=0$

Putting the value in the equation.

  $=>16+16-32=0$

Simplifying the expression.

  $=>32-32=0$

Hence this result is a success.

Now, for $y=8$

  ${\left(8\right)}^2-4\left(8\right)-32=0$

Putting the value in the equation.

  $=>64-32-32=0$

Simplifying the expression.

  $=>64-64=0$

Hence this result is a success.