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Simplifying (4x2 + -31x + 103) + (3x2 + 10x + 7) = 180 Reorder the terms: (103 + -31x + 4x2) + (3x2 + 10x + 7) = 180 Remove parenthesis around (103 + -31x + 4x2) 103 + -31x + 4x2 + (3x2 + 10x + 7) = 180 Reorder the terms: 103 + -31x + 4x2 + (7 + 10x + 3x2) = 180 Remove parenthesis around (7 + 10x + 3x2) 103 + -31x + 4x2 + 7 + 10x + 3x2 = 180 Reorder the terms: 103 + 7 + -31x + 10x + 4x2 + 3x2 = 180 Combine like terms: 103 + 7 = 110 110 + -31x + 10x + 4x2 + 3x2 = 180 Combine like terms: -31x + 10x = -21x 110 + -21x + 4x2 + 3x2 = 180 Combine like terms: 4x2 + 3x2 = 7x2 110 + -21x + 7x2 = 180 Solving 110 + -21x + 7x2 = 180 Solving for variable 'x'. Reorder the terms: 110 + -180 + -21x + 7x2 = 180 + -180 Combine like terms: 110 + -180 = -70 -70 + -21x + 7x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -70 + -21x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-10 + -3x + x2) = 0 Factor a trinomial. 7((-2 + -1x)(5 + -1x)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-2, 5}
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