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Simplifying 34y2 + 46y + -39 = 0 Reorder the terms: -39 + 46y + 34y2 = 0 Solving -39 + 46y + 34y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 34 the coefficient of the squared term: Divide each side by '34'. -1.147058824 + 1.352941176y + y2 = 0 Move the constant term to the right: Add '1.147058824' to each side of the equation. -1.147058824 + 1.352941176y + 1.147058824 + y2 = 0 + 1.147058824 Reorder the terms: -1.147058824 + 1.147058824 + 1.352941176y + y2 = 0 + 1.147058824 Combine like terms: -1.147058824 + 1.147058824 = 0.000000000 0.000000000 + 1.352941176y + y2 = 0 + 1.147058824 1.352941176y + y2 = 0 + 1.147058824 Combine like terms: 0 + 1.147058824 = 1.147058824 1.352941176y + y2 = 1.147058824 The y term is 1.352941176y. Take half its coefficient (0.676470588). Square it (0.4576124564) and add it to both sides. Add '0.4576124564' to each side of the equation. 1.352941176y + 0.4576124564 + y2 = 1.147058824 + 0.4576124564 Reorder the terms: 0.4576124564 + 1.352941176y + y2 = 1.147058824 + 0.4576124564 Combine like terms: 1.147058824 + 0.4576124564 = 1.6046712804 0.4576124564 + 1.352941176y + y2 = 1.6046712804 Factor a perfect square on the left side: (y + 0.676470588)(y + 0.676470588) = 1.6046712804 Calculate the square root of the right side: 1.266756204 Break this problem into two subproblems by setting (y + 0.676470588) equal to 1.266756204 and -1.266756204.Subproblem 1
y + 0.676470588 = 1.266756204 Simplifying y + 0.676470588 = 1.266756204 Reorder the terms: 0.676470588 + y = 1.266756204 Solving 0.676470588 + y = 1.266756204 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.676470588' to each side of the equation. 0.676470588 + -0.676470588 + y = 1.266756204 + -0.676470588 Combine like terms: 0.676470588 + -0.676470588 = 0.000000000 0.000000000 + y = 1.266756204 + -0.676470588 y = 1.266756204 + -0.676470588 Combine like terms: 1.266756204 + -0.676470588 = 0.590285616 y = 0.590285616 Simplifying y = 0.590285616Subproblem 2
y + 0.676470588 = -1.266756204 Simplifying y + 0.676470588 = -1.266756204 Reorder the terms: 0.676470588 + y = -1.266756204 Solving 0.676470588 + y = -1.266756204 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.676470588' to each side of the equation. 0.676470588 + -0.676470588 + y = -1.266756204 + -0.676470588 Combine like terms: 0.676470588 + -0.676470588 = 0.000000000 0.000000000 + y = -1.266756204 + -0.676470588 y = -1.266756204 + -0.676470588 Combine like terms: -1.266756204 + -0.676470588 = -1.943226792 y = -1.943226792 Simplifying y = -1.943226792Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.590285616, -1.943226792}
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