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Simplifying 56 = 2y2 + 6y + -4 Reorder the terms: 56 = -4 + 6y + 2y2 Solving 56 = -4 + 6y + 2y2 Solving for variable 'y'. Combine like terms: 56 + 4 = 60 60 + -6y + -2y2 = -4 + 6y + 2y2 + 4 + -6y + -2y2 Reorder the terms: 60 + -6y + -2y2 = -4 + 4 + 6y + -6y + 2y2 + -2y2 Combine like terms: -4 + 4 = 0 60 + -6y + -2y2 = 0 + 6y + -6y + 2y2 + -2y2 60 + -6y + -2y2 = 6y + -6y + 2y2 + -2y2 Combine like terms: 6y + -6y = 0 60 + -6y + -2y2 = 0 + 2y2 + -2y2 60 + -6y + -2y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 60 + -6y + -2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(30 + -3y + -1y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(30 + -3y + -1y2)' equal to zero and attempt to solve: Simplifying 30 + -3y + -1y2 = 0 Solving 30 + -3y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + 3y + y2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 3y + 30 + y2 = 0 + 30 Reorder the terms: -30 + 30 + 3y + y2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 3y + y2 = 0 + 30 3y + y2 = 0 + 30 Combine like terms: 0 + 30 = 30 3y + y2 = 30 The y term is 3y. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3y + 2.25 + y2 = 30 + 2.25 Reorder the terms: 2.25 + 3y + y2 = 30 + 2.25 Combine like terms: 30 + 2.25 = 32.25 2.25 + 3y + y2 = 32.25 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (y + 1.5) equal to 5.678908346 and -5.678908346.Subproblem 1
y + 1.5 = 5.678908346 Simplifying y + 1.5 = 5.678908346 Reorder the terms: 1.5 + y = 5.678908346 Solving 1.5 + y = 5.678908346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 5.678908346 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 5.678908346 + -1.5 y = 5.678908346 + -1.5 Combine like terms: 5.678908346 + -1.5 = 4.178908346 y = 4.178908346 Simplifying y = 4.178908346Subproblem 2
y + 1.5 = -5.678908346 Simplifying y + 1.5 = -5.678908346 Reorder the terms: 1.5 + y = -5.678908346 Solving 1.5 + y = -5.678908346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = -5.678908346 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -5.678908346 + -1.5 y = -5.678908346 + -1.5 Combine like terms: -5.678908346 + -1.5 = -7.178908346 y = -7.178908346 Simplifying y = -7.178908346Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.178908346, -7.178908346}Solution
y = {4.178908346, -7.178908346}
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