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Simplifying -80x2 + 120x + 610 = 660 Reorder the terms: 610 + 120x + -80x2 = 660 Solving 610 + 120x + -80x2 = 660 Solving for variable 'x'. Reorder the terms: 610 + -660 + 120x + -80x2 = 660 + -660 Combine like terms: 610 + -660 = -50 -50 + 120x + -80x2 = 660 + -660 Combine like terms: 660 + -660 = 0 -50 + 120x + -80x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-5 + 12x + -8x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-5 + 12x + -8x2)' equal to zero and attempt to solve: Simplifying -5 + 12x + -8x2 = 0 Solving -5 + 12x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.625 + -1.5x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -1.5x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -1.5x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -1.5x + x2 = 0 + -0.625 -1.5x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -1.5x + x2 = -0.625 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -0.625 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -0.625 + 0.5625 Combine like terms: -0.625 + 0.5625 = -0.0625 0.5625 + -1.5x + x2 = -0.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -0.0625 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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