Chapter 9, Problem 36SGR

To determine

To solve the given equation by factoring.

Answer to Problem 36SGR

The value of w is $\frac{3}{2}$ .

Explanation of Solution

Given information :

The equation provided is $4w^2+9=12w$ . This can be written as $4w^2-12w+9=0$ .

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 :

  $4w^2-12w+9=0$

Equation to be solved.

  $=>4w^2-6w-6w+9=0$

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

  $=>2w\left(2w-3\right)-3\left(2w-3\right)=0$

Arranging the common factors.

  $=>\left(2w-3\right)\left(2w-3\right)=0$

  $=>{\left(2w-3\right)}^2=0$

The two factors of the function.

Now, the root is:

  $2w-3=0$

Using zero-product property.

  $=>w=\frac{3}{2}$

Thus, the value of w is $\frac{3}{2}$ .

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

For $w=\frac{3}{2}$

  $4{\left(\frac{3}{2}\right)}^2-12\left(\frac{3}{2}\right)+9=0$

Putting the value in the equation.

  $=>9-18+9=0$

Simplifying the expression.

  $=>18-18=0$

Hence this result is a success.