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Simplifying -6x2 + -7x + -15 = 0 Reorder the terms: -15 + -7x + -6x2 = 0 Solving -15 + -7x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 7x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 7x + 6x2)' equal to zero and attempt to solve: Simplifying 15 + 7x + 6x2 = 0 Solving 15 + 7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.5 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 1.166666667x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 1.166666667x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 1.166666667x + x2 = 0 + -2.5 1.166666667x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 1.166666667x + x2 = -2.5 The x term is 1.166666667x. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667x + 0.3402777780 + x2 = -2.5 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = -2.5 + 0.3402777780 Combine like terms: -2.5 + 0.3402777780 = -2.159722222 0.3402777780 + 1.166666667x + x2 = -2.159722222 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = -2.159722222 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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