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Simplifying (x)(x + 3) + -1(x + -1)(2x + 6) = 176 Reorder the terms: x(3 + x) + -1(x + -1)(2x + 6) = 176 (3 * x + x * x) + -1(x + -1)(2x + 6) = 176 (3x + x2) + -1(x + -1)(2x + 6) = 176 Reorder the terms: 3x + x2 + -1(-1 + x)(2x + 6) = 176 Reorder the terms: 3x + x2 + -1(-1 + x)(6 + 2x) = 176 Multiply (-1 + x) * (6 + 2x) 3x + x2 + -1(-1(6 + 2x) + x(6 + 2x)) = 176 3x + x2 + -1((6 * -1 + 2x * -1) + x(6 + 2x)) = 176 3x + x2 + -1((-6 + -2x) + x(6 + 2x)) = 176 3x + x2 + -1(-6 + -2x + (6 * x + 2x * x)) = 176 3x + x2 + -1(-6 + -2x + (6x + 2x2)) = 176 Combine like terms: -2x + 6x = 4x 3x + x2 + -1(-6 + 4x + 2x2) = 176 3x + x2 + (-6 * -1 + 4x * -1 + 2x2 * -1) = 176 3x + x2 + (6 + -4x + -2x2) = 176 Reorder the terms: 6 + 3x + -4x + x2 + -2x2 = 176 Combine like terms: 3x + -4x = -1x 6 + -1x + x2 + -2x2 = 176 Combine like terms: x2 + -2x2 = -1x2 6 + -1x + -1x2 = 176 Solving 6 + -1x + -1x2 = 176 Solving for variable 'x'. Reorder the terms: 6 + -176 + -1x + -1x2 = 176 + -176 Combine like terms: 6 + -176 = -170 -170 + -1x + -1x2 = 176 + -176 Combine like terms: 176 + -176 = 0 -170 + -1x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(170 + x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(170 + x + x2)' equal to zero and attempt to solve: Simplifying 170 + x + x2 = 0 Solving 170 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-170' to each side of the equation. 170 + x + -170 + x2 = 0 + -170 Reorder the terms: 170 + -170 + x + x2 = 0 + -170 Combine like terms: 170 + -170 = 0 0 + x + x2 = 0 + -170 x + x2 = 0 + -170 Combine like terms: 0 + -170 = -170 x + x2 = -170 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = -170 + 0.25 Reorder the terms: 0.25 + x + x2 = -170 + 0.25 Combine like terms: -170 + 0.25 = -169.75 0.25 + x + x2 = -169.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -169.75 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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