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Simplifying -5(2x + 1) * 3x = 37 Reorder the terms: -5(1 + 2x) * 3x = 37 Reorder the terms for easier multiplication: -5 * 3x(1 + 2x) = 37 Multiply -5 * 3 -15x(1 + 2x) = 37 (1 * -15x + 2x * -15x) = 37 (-15x + -30x2) = 37 Solving -15x + -30x2 = 37 Solving for variable 'x'. Reorder the terms: -37 + -15x + -30x2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + -15x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(37 + 15x + 30x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(37 + 15x + 30x2)' equal to zero and attempt to solve: Simplifying 37 + 15x + 30x2 = 0 Solving 37 + 15x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 1.233333333 + 0.5x + x2 = 0.0 Move the constant term to the right: Add '-1.233333333' to each side of the equation. 1.233333333 + 0.5x + -1.233333333 + x2 = 0.0 + -1.233333333 Reorder the terms: 1.233333333 + -1.233333333 + 0.5x + x2 = 0.0 + -1.233333333 Combine like terms: 1.233333333 + -1.233333333 = 0.000000000 0.000000000 + 0.5x + x2 = 0.0 + -1.233333333 0.5x + x2 = 0.0 + -1.233333333 Combine like terms: 0.0 + -1.233333333 = -1.233333333 0.5x + x2 = -1.233333333 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -1.233333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -1.233333333 + 0.0625 Combine like terms: -1.233333333 + 0.0625 = -1.170833333 0.0625 + 0.5x + x2 = -1.170833333 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -1.170833333 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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