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Simplifying -4x2 + 30x + -76 = 0 Reorder the terms: -76 + 30x + -4x2 = 0 Solving -76 + 30x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-38 + 15x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-38 + 15x + -2x2)' equal to zero and attempt to solve: Simplifying -38 + 15x + -2x2 = 0 Solving -38 + 15x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 19 + -7.5x + x2 = 0 Move the constant term to the right: Add '-19' to each side of the equation. 19 + -7.5x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + -7.5x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -7.5x + x2 = 0 + -19 -7.5x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 -7.5x + x2 = -19 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -19 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -19 + 14.0625 Combine like terms: -19 + 14.0625 = -4.9375 14.0625 + -7.5x + x2 = -4.9375 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = -4.9375 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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