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Simplifying 14x + -2x2 = 120 + -6x Solving 14x + -2x2 = 120 + -6x Solving for variable 'x'. Reorder the terms: -120 + 14x + 6x + -2x2 = 120 + -6x + -120 + 6x Combine like terms: 14x + 6x = 20x -120 + 20x + -2x2 = 120 + -6x + -120 + 6x Reorder the terms: -120 + 20x + -2x2 = 120 + -120 + -6x + 6x Combine like terms: 120 + -120 = 0 -120 + 20x + -2x2 = 0 + -6x + 6x -120 + 20x + -2x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -120 + 20x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + 10x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-60 + 10x + -1x2)' equal to zero and attempt to solve: Simplifying -60 + 10x + -1x2 = 0 Solving -60 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 60 + -10x + x2 = 0 Move the constant term to the right: Add '-60' to each side of the equation. 60 + -10x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -10x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -10x + x2 = 0 + -60 -10x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -10x + x2 = -60 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -60 + 25 Reorder the terms: 25 + -10x + x2 = -60 + 25 Combine like terms: -60 + 25 = -35 25 + -10x + x2 = -35 Factor a perfect square on the left side: (x + -5)(x + -5) = -35 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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