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Simplifying 8y2 + 12y = 42 Reorder the terms: 12y + 8y2 = 42 Solving 12y + 8y2 = 42 Solving for variable 'y'. Reorder the terms: -42 + 12y + 8y2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + 12y + 8y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 6y + 4y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + 6y + 4y2)' equal to zero and attempt to solve: Simplifying -21 + 6y + 4y2 = 0 Solving -21 + 6y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + 1.5y + y2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 1.5y + 5.25 + y2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 1.5y + y2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 1.5y + y2 = 0 + 5.25 1.5y + y2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 1.5y + y2 = 5.25 The y term is 1.5y. 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. 1.5y + 0.5625 + y2 = 5.25 + 0.5625 Reorder the terms: 0.5625 + 1.5y + y2 = 5.25 + 0.5625 Combine like terms: 5.25 + 0.5625 = 5.8125 0.5625 + 1.5y + y2 = 5.8125 Factor a perfect square on the left side: (y + 0.75)(y + 0.75) = 5.8125 Calculate the square root of the right side: 2.41091269 Break this problem into two subproblems by setting (y + 0.75) equal to 2.41091269 and -2.41091269.Subproblem 1
y + 0.75 = 2.41091269 Simplifying y + 0.75 = 2.41091269 Reorder the terms: 0.75 + y = 2.41091269 Solving 0.75 + y = 2.41091269 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y = 2.41091269 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = 2.41091269 + -0.75 y = 2.41091269 + -0.75 Combine like terms: 2.41091269 + -0.75 = 1.66091269 y = 1.66091269 Simplifying y = 1.66091269Subproblem 2
y + 0.75 = -2.41091269 Simplifying y + 0.75 = -2.41091269 Reorder the terms: 0.75 + y = -2.41091269 Solving 0.75 + y = -2.41091269 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y = -2.41091269 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = -2.41091269 + -0.75 y = -2.41091269 + -0.75 Combine like terms: -2.41091269 + -0.75 = -3.16091269 y = -3.16091269 Simplifying y = -3.16091269Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.66091269, -3.16091269}Solution
y = {1.66091269, -3.16091269}
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