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Simplifying 3(x + -1) + -2(x2 + 2x + 3) + -5(x + 7) = 0 Reorder the terms: 3(-1 + x) + -2(x2 + 2x + 3) + -5(x + 7) = 0 (-1 * 3 + x * 3) + -2(x2 + 2x + 3) + -5(x + 7) = 0 (-3 + 3x) + -2(x2 + 2x + 3) + -5(x + 7) = 0 Reorder the terms: -3 + 3x + -2(3 + 2x + x2) + -5(x + 7) = 0 -3 + 3x + (3 * -2 + 2x * -2 + x2 * -2) + -5(x + 7) = 0 -3 + 3x + (-6 + -4x + -2x2) + -5(x + 7) = 0 Reorder the terms: -3 + 3x + -6 + -4x + -2x2 + -5(7 + x) = 0 -3 + 3x + -6 + -4x + -2x2 + (7 * -5 + x * -5) = 0 -3 + 3x + -6 + -4x + -2x2 + (-35 + -5x) = 0 Reorder the terms: -3 + -6 + -35 + 3x + -4x + -5x + -2x2 = 0 Combine like terms: -3 + -6 = -9 -9 + -35 + 3x + -4x + -5x + -2x2 = 0 Combine like terms: -9 + -35 = -44 -44 + 3x + -4x + -5x + -2x2 = 0 Combine like terms: 3x + -4x = -1x -44 + -1x + -5x + -2x2 = 0 Combine like terms: -1x + -5x = -6x -44 + -6x + -2x2 = 0 Solving -44 + -6x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(22 + 3x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(22 + 3x + x2)' equal to zero and attempt to solve: Simplifying 22 + 3x + x2 = 0 Solving 22 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 3x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + 3x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 3x + x2 = 0 + -22 3x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 3x + x2 = -22 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -22 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -22 + 2.25 Combine like terms: -22 + 2.25 = -19.75 2.25 + 3x + x2 = -19.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -19.75 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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