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Simplifying -3x2 + -14x + -7 = (x + -1)(x + 1) Reorder the terms: -7 + -14x + -3x2 = (x + -1)(x + 1) Reorder the terms: -7 + -14x + -3x2 = (-1 + x)(x + 1) Reorder the terms: -7 + -14x + -3x2 = (-1 + x)(1 + x) Multiply (-1 + x) * (1 + x) -7 + -14x + -3x2 = (-1(1 + x) + x(1 + x)) -7 + -14x + -3x2 = ((1 * -1 + x * -1) + x(1 + x)) -7 + -14x + -3x2 = ((-1 + -1x) + x(1 + x)) -7 + -14x + -3x2 = (-1 + -1x + (1 * x + x * x)) -7 + -14x + -3x2 = (-1 + -1x + (1x + x2)) Combine like terms: -1x + 1x = 0 -7 + -14x + -3x2 = (-1 + 0 + x2) -7 + -14x + -3x2 = (-1 + x2) Solving -7 + -14x + -3x2 = -1 + x2 Solving for variable 'x'. Reorder the terms: -7 + 1 + -14x + -3x2 + -1x2 = -1 + x2 + 1 + -1x2 Combine like terms: -7 + 1 = -6 -6 + -14x + -3x2 + -1x2 = -1 + x2 + 1 + -1x2 Combine like terms: -3x2 + -1x2 = -4x2 -6 + -14x + -4x2 = -1 + x2 + 1 + -1x2 Reorder the terms: -6 + -14x + -4x2 = -1 + 1 + x2 + -1x2 Combine like terms: -1 + 1 = 0 -6 + -14x + -4x2 = 0 + x2 + -1x2 -6 + -14x + -4x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -6 + -14x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(3 + 7x + 2x2) = 0 Factor a trinomial. -2((3 + x)(1 + 2x)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-3, -0.5}
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