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Simplifying 24x + -12x2 + -120 = 0 Reorder the terms: -120 + 24x + -12x2 = 0 Solving -120 + 24x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-10 + 2x + -1x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-10 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying -10 + 2x + -1x2 = 0 Solving -10 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -2x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -2x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -2x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -2x + x2 = 0 + -10 -2x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -2x + x2 = -10 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -10 + 1 Reorder the terms: 1 + -2x + x2 = -10 + 1 Combine like terms: -10 + 1 = -9 1 + -2x + x2 = -9 Factor a perfect square on the left side: (x + -1)(x + -1) = -9 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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