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Simplifying -2x(x + 3) + 5(x + -2) = 3(x + 6) + -2x Reorder the terms: -2x(3 + x) + 5(x + -2) = 3(x + 6) + -2x (3 * -2x + x * -2x) + 5(x + -2) = 3(x + 6) + -2x (-6x + -2x2) + 5(x + -2) = 3(x + 6) + -2x Reorder the terms: -6x + -2x2 + 5(-2 + x) = 3(x + 6) + -2x -6x + -2x2 + (-2 * 5 + x * 5) = 3(x + 6) + -2x -6x + -2x2 + (-10 + 5x) = 3(x + 6) + -2x Reorder the terms: -10 + -6x + 5x + -2x2 = 3(x + 6) + -2x Combine like terms: -6x + 5x = -1x -10 + -1x + -2x2 = 3(x + 6) + -2x Reorder the terms: -10 + -1x + -2x2 = 3(6 + x) + -2x -10 + -1x + -2x2 = (6 * 3 + x * 3) + -2x -10 + -1x + -2x2 = (18 + 3x) + -2x Combine like terms: 3x + -2x = 1x -10 + -1x + -2x2 = 18 + 1x Solving -10 + -1x + -2x2 = 18 + 1x Solving for variable 'x'. Reorder the terms: -10 + -18 + -1x + -1x + -2x2 = 18 + 1x + -18 + -1x Combine like terms: -10 + -18 = -28 -28 + -1x + -1x + -2x2 = 18 + 1x + -18 + -1x Combine like terms: -1x + -1x = -2x -28 + -2x + -2x2 = 18 + 1x + -18 + -1x Reorder the terms: -28 + -2x + -2x2 = 18 + -18 + 1x + -1x Combine like terms: 18 + -18 = 0 -28 + -2x + -2x2 = 0 + 1x + -1x -28 + -2x + -2x2 = 1x + -1x Combine like terms: 1x + -1x = 0 -28 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(14 + x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(14 + x + x2)' equal to zero and attempt to solve: Simplifying 14 + x + x2 = 0 Solving 14 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + x + x2 = 0 + -14 x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 x + x2 = -14 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = -14 + 0.25 Reorder the terms: 0.25 + x + x2 = -14 + 0.25 Combine like terms: -14 + 0.25 = -13.75 0.25 + x + x2 = -13.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -13.75 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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