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Simplifying 5(x + -1) + -3(x2 + 4x + 5) + -8(x + 8) = 0 Reorder the terms: 5(-1 + x) + -3(x2 + 4x + 5) + -8(x + 8) = 0 (-1 * 5 + x * 5) + -3(x2 + 4x + 5) + -8(x + 8) = 0 (-5 + 5x) + -3(x2 + 4x + 5) + -8(x + 8) = 0 Reorder the terms: -5 + 5x + -3(5 + 4x + x2) + -8(x + 8) = 0 -5 + 5x + (5 * -3 + 4x * -3 + x2 * -3) + -8(x + 8) = 0 -5 + 5x + (-15 + -12x + -3x2) + -8(x + 8) = 0 Reorder the terms: -5 + 5x + -15 + -12x + -3x2 + -8(8 + x) = 0 -5 + 5x + -15 + -12x + -3x2 + (8 * -8 + x * -8) = 0 -5 + 5x + -15 + -12x + -3x2 + (-64 + -8x) = 0 Reorder the terms: -5 + -15 + -64 + 5x + -12x + -8x + -3x2 = 0 Combine like terms: -5 + -15 = -20 -20 + -64 + 5x + -12x + -8x + -3x2 = 0 Combine like terms: -20 + -64 = -84 -84 + 5x + -12x + -8x + -3x2 = 0 Combine like terms: 5x + -12x = -7x -84 + -7x + -8x + -3x2 = 0 Combine like terms: -7x + -8x = -15x -84 + -15x + -3x2 = 0 Solving -84 + -15x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-3'. -3(28 + 5x + x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(28 + 5x + x2)' equal to zero and attempt to solve: Simplifying 28 + 5x + x2 = 0 Solving 28 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + 5x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + 5x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + 5x + x2 = 0 + -28 5x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 5x + x2 = -28 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 = -28 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -28 + 6.25 Combine like terms: -28 + 6.25 = -21.75 6.25 + 5x + x2 = -21.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -21.75 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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