Question 21170: Could someone please help me with this problem?
5x^2=26x+24
thanks so much!!
Answer by Here2Help(19)   (Show Source):
You can put this solution on YOUR website! Here you go:
Original problem:
5x2 = 26x + 24
Reorder the terms:
5x2 = 24 + 26x
Solving
5x2 = 24 + 26x
Solving for variable 'x'.
Reorder the terms:
-24 + -26x + 5x2 = 24 + 26x + -24 + -26x
Reorder the terms:
-24 + -26x + 5x2 = 24 + -24 + 26x + -26x
Combine like terms: 24 + -24 = 0
-24 + -26x + 5x2 = 0 + 26x + -26x
-24 + -26x + 5x2 = 26x + -26x
Combine like terms: 26x + -26x = 0
-24 + -26x + 5x2 = 0
Factor a trinomial.
(-4 + -5x)(6 + -1x) = 0
Subproblem 1
Set the factor '(-4 + -5x)' equal to zero and attempt to solve:
Simplifying
-4 + -5x = 0
Solving
-4 + -5x = 0
Move all terms containing x to the left, all other terms to the right.
Add '4' to each side of the equation.
-4 + 4 + -5x = 0 + 4
Combine like terms: -4 + 4 = 0
0 + -5x = 0 + 4
-5x = 0 + 4
Combine like terms: 0 + 4 = 4
-5x = 4
Divide each side by '-5'.
x = -0.8
Simplifying
x = -0.8
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:
Simplifying
6 + -1x = 0
Solving
6 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6
Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6
Combine like terms: 0 + -6 = -6
-1x = -6
Divide each side by '-1'.
x = 6
Simplifying
x = 6
Solution x = {-0.8, 6}
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