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Simplifying 5x(-12x + -6) = 7x + 21 Reorder the terms: 5x(-6 + -12x) = 7x + 21 (-6 * 5x + -12x * 5x) = 7x + 21 (-30x + -60x2) = 7x + 21 Reorder the terms: -30x + -60x2 = 21 + 7x Solving -30x + -60x2 = 21 + 7x Solving for variable 'x'. Reorder the terms: -21 + -30x + -7x + -60x2 = 21 + 7x + -21 + -7x Combine like terms: -30x + -7x = -37x -21 + -37x + -60x2 = 21 + 7x + -21 + -7x Reorder the terms: -21 + -37x + -60x2 = 21 + -21 + 7x + -7x Combine like terms: 21 + -21 = 0 -21 + -37x + -60x2 = 0 + 7x + -7x -21 + -37x + -60x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -21 + -37x + -60x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(21 + 37x + 60x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(21 + 37x + 60x2)' equal to zero and attempt to solve: Simplifying 21 + 37x + 60x2 = 0 Solving 21 + 37x + 60x2 = 0 Begin completing the square. Divide all terms by 60 the coefficient of the squared term: Divide each side by '60'. 0.35 + 0.6166666667x + x2 = 0.0 Move the constant term to the right: Add '-0.35' to each side of the equation. 0.35 + 0.6166666667x + -0.35 + x2 = 0.0 + -0.35 Reorder the terms: 0.35 + -0.35 + 0.6166666667x + x2 = 0.0 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + 0.6166666667x + x2 = 0.0 + -0.35 0.6166666667x + x2 = 0.0 + -0.35 Combine like terms: 0.0 + -0.35 = -0.35 0.6166666667x + x2 = -0.35 The x term is 0.6166666667x. Take half its coefficient (0.3083333334). Square it (0.09506944449) and add it to both sides. Add '0.09506944449' to each side of the equation. 0.6166666667x + 0.09506944449 + x2 = -0.35 + 0.09506944449 Reorder the terms: 0.09506944449 + 0.6166666667x + x2 = -0.35 + 0.09506944449 Combine like terms: -0.35 + 0.09506944449 = -0.25493055551 0.09506944449 + 0.6166666667x + x2 = -0.25493055551 Factor a perfect square on the left side: (x + 0.3083333334)(x + 0.3083333334) = -0.25493055551 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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