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Simplifying -31y2 + -12y = 232 Reorder the terms: -12y + -31y2 = 232 Solving -12y + -31y2 = 232 Solving for variable 'y'. Reorder the terms: -232 + -12y + -31y2 = 232 + -232 Combine like terms: 232 + -232 = 0 -232 + -12y + -31y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(232 + 12y + 31y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(232 + 12y + 31y2)' equal to zero and attempt to solve: Simplifying 232 + 12y + 31y2 = 0 Solving 232 + 12y + 31y2 = 0 Begin completing the square. Divide all terms by 31 the coefficient of the squared term: Divide each side by '31'. 7.483870968 + 0.3870967742y + y2 = 0 Move the constant term to the right: Add '-7.483870968' to each side of the equation. 7.483870968 + 0.3870967742y + -7.483870968 + y2 = 0 + -7.483870968 Reorder the terms: 7.483870968 + -7.483870968 + 0.3870967742y + y2 = 0 + -7.483870968 Combine like terms: 7.483870968 + -7.483870968 = 0.000000000 0.000000000 + 0.3870967742y + y2 = 0 + -7.483870968 0.3870967742y + y2 = 0 + -7.483870968 Combine like terms: 0 + -7.483870968 = -7.483870968 0.3870967742y + y2 = -7.483870968 The y term is 0.3870967742y. Take half its coefficient (0.1935483871). Square it (0.03746097815) and add it to both sides. Add '0.03746097815' to each side of the equation. 0.3870967742y + 0.03746097815 + y2 = -7.483870968 + 0.03746097815 Reorder the terms: 0.03746097815 + 0.3870967742y + y2 = -7.483870968 + 0.03746097815 Combine like terms: -7.483870968 + 0.03746097815 = -7.44640998985 0.03746097815 + 0.3870967742y + y2 = -7.44640998985 Factor a perfect square on the left side: (y + 0.1935483871)(y + 0.1935483871) = -7.44640998985 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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