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Simplifying 8y2 + 28y + -49 = 37 Reorder the terms: -49 + 28y + 8y2 = 37 Solving -49 + 28y + 8y2 = 37 Solving for variable 'y'. Reorder the terms: -49 + -37 + 28y + 8y2 = 37 + -37 Combine like terms: -49 + -37 = -86 -86 + 28y + 8y2 = 37 + -37 Combine like terms: 37 + -37 = 0 -86 + 28y + 8y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-43 + 14y + 4y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-43 + 14y + 4y2)' equal to zero and attempt to solve: Simplifying -43 + 14y + 4y2 = 0 Solving -43 + 14y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10.75 + 3.5y + y2 = 0 Move the constant term to the right: Add '10.75' to each side of the equation. -10.75 + 3.5y + 10.75 + y2 = 0 + 10.75 Reorder the terms: -10.75 + 10.75 + 3.5y + y2 = 0 + 10.75 Combine like terms: -10.75 + 10.75 = 0.00 0.00 + 3.5y + y2 = 0 + 10.75 3.5y + y2 = 0 + 10.75 Combine like terms: 0 + 10.75 = 10.75 3.5y + y2 = 10.75 The y term is 3.5y. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5y + 3.0625 + y2 = 10.75 + 3.0625 Reorder the terms: 3.0625 + 3.5y + y2 = 10.75 + 3.0625 Combine like terms: 10.75 + 3.0625 = 13.8125 3.0625 + 3.5y + y2 = 13.8125 Factor a perfect square on the left side: (y + 1.75)(y + 1.75) = 13.8125 Calculate the square root of the right side: 3.716517187 Break this problem into two subproblems by setting (y + 1.75) equal to 3.716517187 and -3.716517187.Subproblem 1
y + 1.75 = 3.716517187 Simplifying y + 1.75 = 3.716517187 Reorder the terms: 1.75 + y = 3.716517187 Solving 1.75 + y = 3.716517187 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = 3.716517187 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = 3.716517187 + -1.75 y = 3.716517187 + -1.75 Combine like terms: 3.716517187 + -1.75 = 1.966517187 y = 1.966517187 Simplifying y = 1.966517187Subproblem 2
y + 1.75 = -3.716517187 Simplifying y + 1.75 = -3.716517187 Reorder the terms: 1.75 + y = -3.716517187 Solving 1.75 + y = -3.716517187 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = -3.716517187 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = -3.716517187 + -1.75 y = -3.716517187 + -1.75 Combine like terms: -3.716517187 + -1.75 = -5.466517187 y = -5.466517187 Simplifying y = -5.466517187Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.966517187, -5.466517187}Solution
y = {1.966517187, -5.466517187}
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