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Simplifying 0 = 6x2 + 13x + 45 Reorder the terms: 0 = 45 + 13x + 6x2 Solving 0 = 45 + 13x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -45 = -45 -45 + -13x + -6x2 = 45 + 13x + 6x2 + -45 + -13x + -6x2 Reorder the terms: -45 + -13x + -6x2 = 45 + -45 + 13x + -13x + 6x2 + -6x2 Combine like terms: 45 + -45 = 0 -45 + -13x + -6x2 = 0 + 13x + -13x + 6x2 + -6x2 -45 + -13x + -6x2 = 13x + -13x + 6x2 + -6x2 Combine like terms: 13x + -13x = 0 -45 + -13x + -6x2 = 0 + 6x2 + -6x2 -45 + -13x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -45 + -13x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(45 + 13x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(45 + 13x + 6x2)' equal to zero and attempt to solve: Simplifying 45 + 13x + 6x2 = 0 Solving 45 + 13x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 7.5 + 2.166666667x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 2.166666667x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 2.166666667x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 2.166666667x + x2 = 0 + -7.5 2.166666667x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 2.166666667x + x2 = -7.5 The x term is 2.166666667x. Take half its coefficient (1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. 2.166666667x + 1.173611113 + x2 = -7.5 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667x + x2 = -7.5 + 1.173611113 Combine like terms: -7.5 + 1.173611113 = -6.326388887 1.173611113 + 2.166666667x + x2 = -6.326388887 Factor a perfect square on the left side: (x + 1.083333334)(x + 1.083333334) = -6.326388887 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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