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Simplifying 2x + 8 + -1(x + 10)(x + 2) = 68 Reorder the terms: 2x + 8 + -1(10 + x)(x + 2) = 68 Reorder the terms: 2x + 8 + -1(10 + x)(2 + x) = 68 Multiply (10 + x) * (2 + x) 2x + 8 + -1(10(2 + x) + x(2 + x)) = 68 2x + 8 + -1((2 * 10 + x * 10) + x(2 + x)) = 68 2x + 8 + -1((20 + 10x) + x(2 + x)) = 68 2x + 8 + -1(20 + 10x + (2 * x + x * x)) = 68 2x + 8 + -1(20 + 10x + (2x + x2)) = 68 Combine like terms: 10x + 2x = 12x 2x + 8 + -1(20 + 12x + x2) = 68 2x + 8 + (20 * -1 + 12x * -1 + x2 * -1) = 68 2x + 8 + (-20 + -12x + -1x2) = 68 Reorder the terms: 8 + -20 + 2x + -12x + -1x2 = 68 Combine like terms: 8 + -20 = -12 -12 + 2x + -12x + -1x2 = 68 Combine like terms: 2x + -12x = -10x -12 + -10x + -1x2 = 68 Solving -12 + -10x + -1x2 = 68 Solving for variable 'x'. Reorder the terms: -12 + -68 + -10x + -1x2 = 68 + -68 Combine like terms: -12 + -68 = -80 -80 + -10x + -1x2 = 68 + -68 Combine like terms: 68 + -68 = 0 -80 + -10x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(80 + 10x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(80 + 10x + x2)' equal to zero and attempt to solve: Simplifying 80 + 10x + x2 = 0 Solving 80 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + 10x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + 10x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 10x + x2 = 0 + -80 10x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 10x + x2 = -80 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -80 + 25 Reorder the terms: 25 + 10x + x2 = -80 + 25 Combine like terms: -80 + 25 = -55 25 + 10x + x2 = -55 Factor a perfect square on the left side: (x + 5)(x + 5) = -55 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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