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Simplifying -3x2 + -23x + -120 = 0 Reorder the terms: -120 + -23x + -3x2 = 0 Solving -120 + -23x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(120 + 23x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(120 + 23x + 3x2)' equal to zero and attempt to solve: Simplifying 120 + 23x + 3x2 = 0 Solving 120 + 23x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 40 + 7.666666667x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + 7.666666667x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + 7.666666667x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 7.666666667x + x2 = 0 + -40 7.666666667x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 7.666666667x + x2 = -40 The x term is 7.666666667x. Take half its coefficient (3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. 7.666666667x + 14.69444445 + x2 = -40 + 14.69444445 Reorder the terms: 14.69444445 + 7.666666667x + x2 = -40 + 14.69444445 Combine like terms: -40 + 14.69444445 = -25.30555555 14.69444445 + 7.666666667x + x2 = -25.30555555 Factor a perfect square on the left side: (x + 3.833333334)(x + 3.833333334) = -25.30555555 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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