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Simplifying 2x + -4x(x + 3) + -1(3x + 7) = 16 + -5(2x + 3) Reorder the terms: 2x + -4x(3 + x) + -1(3x + 7) = 16 + -5(2x + 3) 2x + (3 * -4x + x * -4x) + -1(3x + 7) = 16 + -5(2x + 3) 2x + (-12x + -4x2) + -1(3x + 7) = 16 + -5(2x + 3) Reorder the terms: 2x + -12x + -4x2 + -1(7 + 3x) = 16 + -5(2x + 3) 2x + -12x + -4x2 + (7 * -1 + 3x * -1) = 16 + -5(2x + 3) 2x + -12x + -4x2 + (-7 + -3x) = 16 + -5(2x + 3) Reorder the terms: -7 + 2x + -12x + -3x + -4x2 = 16 + -5(2x + 3) Combine like terms: 2x + -12x = -10x -7 + -10x + -3x + -4x2 = 16 + -5(2x + 3) Combine like terms: -10x + -3x = -13x -7 + -13x + -4x2 = 16 + -5(2x + 3) Reorder the terms: -7 + -13x + -4x2 = 16 + -5(3 + 2x) -7 + -13x + -4x2 = 16 + (3 * -5 + 2x * -5) -7 + -13x + -4x2 = 16 + (-15 + -10x) Combine like terms: 16 + -15 = 1 -7 + -13x + -4x2 = 1 + -10x Solving -7 + -13x + -4x2 = 1 + -10x Solving for variable 'x'. Reorder the terms: -7 + -1 + -13x + 10x + -4x2 = 1 + -10x + -1 + 10x Combine like terms: -7 + -1 = -8 -8 + -13x + 10x + -4x2 = 1 + -10x + -1 + 10x Combine like terms: -13x + 10x = -3x -8 + -3x + -4x2 = 1 + -10x + -1 + 10x Reorder the terms: -8 + -3x + -4x2 = 1 + -1 + -10x + 10x Combine like terms: 1 + -1 = 0 -8 + -3x + -4x2 = 0 + -10x + 10x -8 + -3x + -4x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -8 + -3x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 3x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying 8 + 3x + 4x2 = 0 Solving 8 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2 + 0.75x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 0.75x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 0.75x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 0.75x + x2 = 0 + -2 0.75x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 0.75x + x2 = -2 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = -2 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -2 + 0.140625 Combine like terms: -2 + 0.140625 = -1.859375 0.140625 + 0.75x + x2 = -1.859375 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -1.859375 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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