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

Studdy Solution

STEP 1

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

STEP 2

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

STEP 3

Now, we need to factor the quadratic equation. This involves finding two numbers that add up to -26 (the coefficient of c) and multiply to -120 (the product of5 and -24).

STEP 4

The two numbers that satisfy these conditions are -20 and6. We can now rewrite the middle term (-26c) as the sum of -20c and6c.
$c^{2} -20c +6c -24 =0$

STEP 5

Next, we group the terms to prepare for factoring by grouping.
$(5c^{2} -20c) + (c -24) =0$

STEP 6

Now, we factor out the greatest common factor from each group.
$5c(c -4) +6(c -4) =0$

STEP 7

Notice that the terms in the parentheses are the same. We can now factor out the common binomial term.
$(5c +6)(c -4) =0$

STEP 8

Now that we have factored the equation, we can set each factor equal to zero and solve for c.
$5c +6 =0$ $c -4 =0$

STEP 9

olving the first equation for c gives $5c = -6$ $c = -6/5$

STEP 10

olving the second equation for c gives $c =4$ So, the solutions to the equation are $c = -6/5$ and $c =4$ .

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