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Simplifying -3(15x2 + 13x + 20) = 0 Reorder the terms: -3(20 + 13x + 15x2) = 0 (20 * -3 + 13x * -3 + 15x2 * -3) = 0 (-60 + -39x + -45x2) = 0 Solving -60 + -39x + -45x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-3'. -3(20 + 13x + 15x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(20 + 13x + 15x2)' equal to zero and attempt to solve: Simplifying 20 + 13x + 15x2 = 0 Solving 20 + 13x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 1.333333333 + 0.8666666667x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 0.8666666667x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 0.8666666667x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 0.8666666667x + x2 = 0 + -1.333333333 0.8666666667x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 0.8666666667x + x2 = -1.333333333 The x term is 0.8666666667x. Take half its coefficient (0.4333333334). Square it (0.1877777778) and add it to both sides. Add '0.1877777778' to each side of the equation. 0.8666666667x + 0.1877777778 + x2 = -1.333333333 + 0.1877777778 Reorder the terms: 0.1877777778 + 0.8666666667x + x2 = -1.333333333 + 0.1877777778 Combine like terms: -1.333333333 + 0.1877777778 = -1.1455555552 0.1877777778 + 0.8666666667x + x2 = -1.1455555552 Factor a perfect square on the left side: (x + 0.4333333334)(x + 0.4333333334) = -1.1455555552 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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