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Simplifying 4x2 + 22x + 23 = -2x + 3 Reorder the terms: 23 + 22x + 4x2 = -2x + 3 Reorder the terms: 23 + 22x + 4x2 = 3 + -2x Solving 23 + 22x + 4x2 = 3 + -2x Solving for variable 'x'. Reorder the terms: 23 + -3 + 22x + 2x + 4x2 = 3 + -2x + -3 + 2x Combine like terms: 23 + -3 = 20 20 + 22x + 2x + 4x2 = 3 + -2x + -3 + 2x Combine like terms: 22x + 2x = 24x 20 + 24x + 4x2 = 3 + -2x + -3 + 2x Reorder the terms: 20 + 24x + 4x2 = 3 + -3 + -2x + 2x Combine like terms: 3 + -3 = 0 20 + 24x + 4x2 = 0 + -2x + 2x 20 + 24x + 4x2 = -2x + 2x Combine like terms: -2x + 2x = 0 20 + 24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 6x + x2) = 0 Factor a trinomial. 4((5 + x)(1 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-5, -1}
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