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Simplifying 3(x + -1) + -2(x2 + 4x + 5) + -5(x + 8) = 0 Reorder the terms: 3(-1 + x) + -2(x2 + 4x + 5) + -5(x + 8) = 0 (-1 * 3 + x * 3) + -2(x2 + 4x + 5) + -5(x + 8) = 0 (-3 + 3x) + -2(x2 + 4x + 5) + -5(x + 8) = 0 Reorder the terms: -3 + 3x + -2(5 + 4x + x2) + -5(x + 8) = 0 -3 + 3x + (5 * -2 + 4x * -2 + x2 * -2) + -5(x + 8) = 0 -3 + 3x + (-10 + -8x + -2x2) + -5(x + 8) = 0 Reorder the terms: -3 + 3x + -10 + -8x + -2x2 + -5(8 + x) = 0 -3 + 3x + -10 + -8x + -2x2 + (8 * -5 + x * -5) = 0 -3 + 3x + -10 + -8x + -2x2 + (-40 + -5x) = 0 Reorder the terms: -3 + -10 + -40 + 3x + -8x + -5x + -2x2 = 0 Combine like terms: -3 + -10 = -13 -13 + -40 + 3x + -8x + -5x + -2x2 = 0 Combine like terms: -13 + -40 = -53 -53 + 3x + -8x + -5x + -2x2 = 0 Combine like terms: 3x + -8x = -5x -53 + -5x + -5x + -2x2 = 0 Combine like terms: -5x + -5x = -10x -53 + -10x + -2x2 = 0 Solving -53 + -10x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(53 + 10x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(53 + 10x + 2x2)' equal to zero and attempt to solve: Simplifying 53 + 10x + 2x2 = 0 Solving 53 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 26.5 + 5x + x2 = 0 Move the constant term to the right: Add '-26.5' to each side of the equation. 26.5 + 5x + -26.5 + x2 = 0 + -26.5 Reorder the terms: 26.5 + -26.5 + 5x + x2 = 0 + -26.5 Combine like terms: 26.5 + -26.5 = 0.0 0.0 + 5x + x2 = 0 + -26.5 5x + x2 = 0 + -26.5 Combine like terms: 0 + -26.5 = -26.5 5x + x2 = -26.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -26.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -26.5 + 6.25 Combine like terms: -26.5 + 6.25 = -20.25 6.25 + 5x + x2 = -20.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -20.25 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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