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Simplifying -36x2 + 18x = 15 Reorder the terms: 18x + -36x2 = 15 Solving 18x + -36x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 18x + -36x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 18x + -36x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 6x + -12x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 6x + -12x2)' equal to zero and attempt to solve: Simplifying -5 + 6x + -12x2 = 0 Solving -5 + 6x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 0.4166666667 + -0.5x + x2 = 0 Move the constant term to the right: Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.5x + -0.4166666667 + x2 = 0 + -0.4166666667 Reorder the terms: 0.4166666667 + -0.4166666667 + -0.5x + x2 = 0 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + -0.5x + x2 = 0 + -0.4166666667 -0.5x + x2 = 0 + -0.4166666667 Combine like terms: 0 + -0.4166666667 = -0.4166666667 -0.5x + x2 = -0.4166666667 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 = -0.4166666667 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = -0.4166666667 + 0.0625 Combine like terms: -0.4166666667 + 0.0625 = -0.3541666667 0.0625 + -0.5x + x2 = -0.3541666667 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = -0.3541666667 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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