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Simplifying -18x2 + 72x + -78 = 0 Reorder the terms: -78 + 72x + -18x2 = 0 Solving -78 + 72x + -18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-13 + 12x + -3x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-13 + 12x + -3x2)' equal to zero and attempt to solve: Simplifying -13 + 12x + -3x2 = 0 Solving -13 + 12x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 4.333333333 + -4x + x2 = 0 Move the constant term to the right: Add '-4.333333333' to each side of the equation. 4.333333333 + -4x + -4.333333333 + x2 = 0 + -4.333333333 Reorder the terms: 4.333333333 + -4.333333333 + -4x + x2 = 0 + -4.333333333 Combine like terms: 4.333333333 + -4.333333333 = 0.000000000 0.000000000 + -4x + x2 = 0 + -4.333333333 -4x + x2 = 0 + -4.333333333 Combine like terms: 0 + -4.333333333 = -4.333333333 -4x + x2 = -4.333333333 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -4.333333333 + 4 Reorder the terms: 4 + -4x + x2 = -4.333333333 + 4 Combine like terms: -4.333333333 + 4 = -0.333333333 4 + -4x + x2 = -0.333333333 Factor a perfect square on the left side: (x + -2)(x + -2) = -0.333333333 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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