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Simplifying 2x + -2(x + 5) * 3x + -9 = 180 Reorder the terms: 2x + -2(5 + x) * 3x + -9 = 180 Reorder the terms for easier multiplication: 2x + -2 * 3x(5 + x) + -9 = 180 Multiply -2 * 3 2x + -6x(5 + x) + -9 = 180 2x + (5 * -6x + x * -6x) + -9 = 180 2x + (-30x + -6x2) + -9 = 180 Reorder the terms: -9 + 2x + -30x + -6x2 = 180 Combine like terms: 2x + -30x = -28x -9 + -28x + -6x2 = 180 Solving -9 + -28x + -6x2 = 180 Solving for variable 'x'. Reorder the terms: -9 + -180 + -28x + -6x2 = 180 + -180 Combine like terms: -9 + -180 = -189 -189 + -28x + -6x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -189 + -28x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(189 + 28x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(189 + 28x + 6x2)' equal to zero and attempt to solve: Simplifying 189 + 28x + 6x2 = 0 Solving 189 + 28x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 31.5 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '-31.5' to each side of the equation. 31.5 + 4.666666667x + -31.5 + x2 = 0 + -31.5 Reorder the terms: 31.5 + -31.5 + 4.666666667x + x2 = 0 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + 4.666666667x + x2 = 0 + -31.5 4.666666667x + x2 = 0 + -31.5 Combine like terms: 0 + -31.5 = -31.5 4.666666667x + x2 = -31.5 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = -31.5 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = -31.5 + 5.444444448 Combine like terms: -31.5 + 5.444444448 = -26.055555552 5.444444448 + 4.666666667x + x2 = -26.055555552 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = -26.055555552 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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