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Simplifying 2y2 + 2y + -13 = 0 Reorder the terms: -13 + 2y + 2y2 = 0 Solving -13 + 2y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + y + y2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + y + 6.5 + y2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + y + y2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y + y2 = 0 + 6.5 y + y2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 y + y2 = 6.5 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + y2 = 6.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + y2 = 6.5 + 0.25 Combine like terms: 6.5 + 0.25 = 6.75 1.25 + y2 = 6.75 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (y + 0.5) equal to 2.598076211 and -2.598076211.Subproblem 1
y + 0.5 = 2.598076211 Simplifying y + 0.5 = 2.598076211 Reorder the terms: 0.5 + y = 2.598076211 Solving 0.5 + y = 2.598076211 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 2.598076211 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 2.598076211 + -0.5 y = 2.598076211 + -0.5 Combine like terms: 2.598076211 + -0.5 = 2.098076211 y = 2.098076211 Simplifying y = 2.098076211Subproblem 2
y + 0.5 = -2.598076211 Simplifying y + 0.5 = -2.598076211 Reorder the terms: 0.5 + y = -2.598076211 Solving 0.5 + y = -2.598076211 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -2.598076211 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -2.598076211 + -0.5 y = -2.598076211 + -0.5 Combine like terms: -2.598076211 + -0.5 = -3.098076211 y = -3.098076211 Simplifying y = -3.098076211Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.098076211, -3.098076211}
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