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Simplifying 6y2 + -46y = 120 Reorder the terms: -46y + 6y2 = 120 Solving -46y + 6y2 = 120 Solving for variable 'y'. Reorder the terms: -120 + -46y + 6y2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + -46y + 6y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + -23y + 3y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-60 + -23y + 3y2)' equal to zero and attempt to solve: Simplifying -60 + -23y + 3y2 = 0 Solving -60 + -23y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -20 + -7.666666667y + y2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -7.666666667y + 20 + y2 = 0 + 20 Reorder the terms: -20 + 20 + -7.666666667y + y2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -7.666666667y + y2 = 0 + 20 -7.666666667y + y2 = 0 + 20 Combine like terms: 0 + 20 = 20 -7.666666667y + y2 = 20 The y term is -7.666666667y. 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. -7.666666667y + 14.69444445 + y2 = 20 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667y + y2 = 20 + 14.69444445 Combine like terms: 20 + 14.69444445 = 34.69444445 14.69444445 + -7.666666667y + y2 = 34.69444445 Factor a perfect square on the left side: (y + -3.833333334)(y + -3.833333334) = 34.69444445 Calculate the square root of the right side: 5.890199016 Break this problem into two subproblems by setting (y + -3.833333334) equal to 5.890199016 and -5.890199016.Subproblem 1
y + -3.833333334 = 5.890199016 Simplifying y + -3.833333334 = 5.890199016 Reorder the terms: -3.833333334 + y = 5.890199016 Solving -3.833333334 + y = 5.890199016 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + y = 5.890199016 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + y = 5.890199016 + 3.833333334 y = 5.890199016 + 3.833333334 Combine like terms: 5.890199016 + 3.833333334 = 9.72353235 y = 9.72353235 Simplifying y = 9.72353235Subproblem 2
y + -3.833333334 = -5.890199016 Simplifying y + -3.833333334 = -5.890199016 Reorder the terms: -3.833333334 + y = -5.890199016 Solving -3.833333334 + y = -5.890199016 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + y = -5.890199016 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + y = -5.890199016 + 3.833333334 y = -5.890199016 + 3.833333334 Combine like terms: -5.890199016 + 3.833333334 = -2.056865682 y = -2.056865682 Simplifying y = -2.056865682Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.72353235, -2.056865682}Solution
y = {9.72353235, -2.056865682}
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