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Simplifying -4x2 + 12x = 58 Reorder the terms: 12x + -4x2 = 58 Solving 12x + -4x2 = 58 Solving for variable 'x'. Reorder the terms: -58 + 12x + -4x2 = 58 + -58 Combine like terms: 58 + -58 = 0 -58 + 12x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-29 + 6x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-29 + 6x + -2x2)' equal to zero and attempt to solve: Simplifying -29 + 6x + -2x2 = 0 Solving -29 + 6x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 14.5 + -3x + x2 = 0 Move the constant term to the right: Add '-14.5' to each side of the equation. 14.5 + -3x + -14.5 + x2 = 0 + -14.5 Reorder the terms: 14.5 + -14.5 + -3x + x2 = 0 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + -3x + x2 = 0 + -14.5 -3x + x2 = 0 + -14.5 Combine like terms: 0 + -14.5 = -14.5 -3x + x2 = -14.5 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -14.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -14.5 + 2.25 Combine like terms: -14.5 + 2.25 = -12.25 2.25 + -3x + x2 = -12.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -12.25 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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