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Simplifying x(x + 5) + -112 = (2x + 15)(x + -2) Reorder the terms: x(5 + x) + -112 = (2x + 15)(x + -2) (5 * x + x * x) + -112 = (2x + 15)(x + -2) (5x + x2) + -112 = (2x + 15)(x + -2) Reorder the terms: -112 + 5x + x2 = (2x + 15)(x + -2) Reorder the terms: -112 + 5x + x2 = (15 + 2x)(x + -2) Reorder the terms: -112 + 5x + x2 = (15 + 2x)(-2 + x) Multiply (15 + 2x) * (-2 + x) -112 + 5x + x2 = (15(-2 + x) + 2x * (-2 + x)) -112 + 5x + x2 = ((-2 * 15 + x * 15) + 2x * (-2 + x)) -112 + 5x + x2 = ((-30 + 15x) + 2x * (-2 + x)) -112 + 5x + x2 = (-30 + 15x + (-2 * 2x + x * 2x)) -112 + 5x + x2 = (-30 + 15x + (-4x + 2x2)) Combine like terms: 15x + -4x = 11x -112 + 5x + x2 = (-30 + 11x + 2x2) Solving -112 + 5x + x2 = -30 + 11x + 2x2 Solving for variable 'x'. Reorder the terms: -112 + 30 + 5x + -11x + x2 + -2x2 = -30 + 11x + 2x2 + 30 + -11x + -2x2 Combine like terms: -112 + 30 = -82 -82 + 5x + -11x + x2 + -2x2 = -30 + 11x + 2x2 + 30 + -11x + -2x2 Combine like terms: 5x + -11x = -6x -82 + -6x + x2 + -2x2 = -30 + 11x + 2x2 + 30 + -11x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -82 + -6x + -1x2 = -30 + 11x + 2x2 + 30 + -11x + -2x2 Reorder the terms: -82 + -6x + -1x2 = -30 + 30 + 11x + -11x + 2x2 + -2x2 Combine like terms: -30 + 30 = 0 -82 + -6x + -1x2 = 0 + 11x + -11x + 2x2 + -2x2 -82 + -6x + -1x2 = 11x + -11x + 2x2 + -2x2 Combine like terms: 11x + -11x = 0 -82 + -6x + -1x2 = 0 + 2x2 + -2x2 -82 + -6x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -82 + -6x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(82 + 6x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(82 + 6x + x2)' equal to zero and attempt to solve: Simplifying 82 + 6x + x2 = 0 Solving 82 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-82' to each side of the equation. 82 + 6x + -82 + x2 = 0 + -82 Reorder the terms: 82 + -82 + 6x + x2 = 0 + -82 Combine like terms: 82 + -82 = 0 0 + 6x + x2 = 0 + -82 6x + x2 = 0 + -82 Combine like terms: 0 + -82 = -82 6x + x2 = -82 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -82 + 9 Reorder the terms: 9 + 6x + x2 = -82 + 9 Combine like terms: -82 + 9 = -73 9 + 6x + x2 = -73 Factor a perfect square on the left side: (x + 3)(x + 3) = -73 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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