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Simplifying 4X2 + -60 = 5X2 + 19X Reorder the terms: -60 + 4X2 = 5X2 + 19X Reorder the terms: -60 + 4X2 = 19X + 5X2 Solving -60 + 4X2 = 19X + 5X2 Solving for variable 'X'. Reorder the terms: -60 + -19X + 4X2 + -5X2 = 19X + 5X2 + -19X + -5X2 Combine like terms: 4X2 + -5X2 = -1X2 -60 + -19X + -1X2 = 19X + 5X2 + -19X + -5X2 Reorder the terms: -60 + -19X + -1X2 = 19X + -19X + 5X2 + -5X2 Combine like terms: 19X + -19X = 0 -60 + -19X + -1X2 = 0 + 5X2 + -5X2 -60 + -19X + -1X2 = 5X2 + -5X2 Combine like terms: 5X2 + -5X2 = 0 -60 + -19X + -1X2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(60 + 19X + X2) = 0 Factor a trinomial. -1((15 + X)(4 + X)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + X)' equal to zero and attempt to solve: Simplifying 15 + X = 0 Solving 15 + X = 0 Move all terms containing X to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + X = 0 + -15 Combine like terms: 15 + -15 = 0 0 + X = 0 + -15 X = 0 + -15 Combine like terms: 0 + -15 = -15 X = -15 Simplifying X = -15Subproblem 2
Set the factor '(4 + X)' equal to zero and attempt to solve: Simplifying 4 + X = 0 Solving 4 + X = 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 + X = 0 + -4 Combine like terms: 4 + -4 = 0 0 + X = 0 + -4 X = 0 + -4 Combine like terms: 0 + -4 = -4 X = -4 Simplifying X = -4Solution
X = {-15, -4}
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