QuestionSolve the equation by factoring: $5 w^{2} = 26 w + 24$ .

Studdy Solution

STEP 1

Assumptions1. We are given the equation $5w^{} =26w +24$ . We are asked to solve this equation by factoring

STEP 2

First, we need to rearrange the equation so that it equals zero. This is because factoring is a method used to solve equations in the form $ax^2 + bx + c =0$ . $5w^{2} -26w -24 =0$

STEP 3

Now, we need to factor the equation. Factoring is the process of breaking down an equation into its simplest terms, or factors. In this case, we are looking for two numbers that multiply to $-120$ (which is $5 \times -24$ ) and add to $-26$ .

STEP 4

The two numbers that satisfy these conditions are $-8$ and $15$ . So, we can rewrite the middle term of the equation as $-8w +15w$ .
$w^{2} -8w +15w -24 =0$

STEP 5

Now, we can factor by grouping. Grouping is a method where we group the terms two at a time and factor out the greatest common factor. $w(5w -8) +3(5w -8) =0$

STEP 6

Now, we can see that the terms in the parentheses are the same. So, we can factor out $5w -8$ .
$(5w -8)(w +3) =0$

STEP 7

Now, we can set each factor equal to zero and solve for $w$ .
$5w - =0 \quad \text{and} \quad w +3 =0$

STEP 8

olve the first equation for $w$ .
$5w =8$ $w = \frac{8}{5}$

STEP 9

olve the second equation for $w$ .
$w = -3$ The solutions to the equation are $w = \frac{8}{5}$ and $w = -3$ .

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