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Simplifying (2x + 11) + -1(x + 5)(3x + 8) = 10 Reorder the terms: (11 + 2x) + -1(x + 5)(3x + 8) = 10 Remove parenthesis around (11 + 2x) 11 + 2x + -1(x + 5)(3x + 8) = 10 Reorder the terms: 11 + 2x + -1(5 + x)(3x + 8) = 10 Reorder the terms: 11 + 2x + -1(5 + x)(8 + 3x) = 10 Multiply (5 + x) * (8 + 3x) 11 + 2x + -1(5(8 + 3x) + x(8 + 3x)) = 10 11 + 2x + -1((8 * 5 + 3x * 5) + x(8 + 3x)) = 10 11 + 2x + -1((40 + 15x) + x(8 + 3x)) = 10 11 + 2x + -1(40 + 15x + (8 * x + 3x * x)) = 10 11 + 2x + -1(40 + 15x + (8x + 3x2)) = 10 Combine like terms: 15x + 8x = 23x 11 + 2x + -1(40 + 23x + 3x2) = 10 11 + 2x + (40 * -1 + 23x * -1 + 3x2 * -1) = 10 11 + 2x + (-40 + -23x + -3x2) = 10 Reorder the terms: 11 + -40 + 2x + -23x + -3x2 = 10 Combine like terms: 11 + -40 = -29 -29 + 2x + -23x + -3x2 = 10 Combine like terms: 2x + -23x = -21x -29 + -21x + -3x2 = 10 Solving -29 + -21x + -3x2 = 10 Solving for variable 'x'. Reorder the terms: -29 + -10 + -21x + -3x2 = 10 + -10 Combine like terms: -29 + -10 = -39 -39 + -21x + -3x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -39 + -21x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(13 + 7x + x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(13 + 7x + x2)' equal to zero and attempt to solve: Simplifying 13 + 7x + x2 = 0 Solving 13 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 7x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 7x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 7x + x2 = 0 + -13 7x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 7x + x2 = -13 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -13 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -13 + 12.25 Combine like terms: -13 + 12.25 = -0.75 12.25 + 7x + x2 = -0.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = -0.75 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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