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Simplifying 13y2 + 14y + -1 = 0 Reorder the terms: -1 + 14y + 13y2 = 0 Solving -1 + 14y + 13y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.07692307692 + 1.076923077y + y2 = 0 Move the constant term to the right: Add '0.07692307692' to each side of the equation. -0.07692307692 + 1.076923077y + 0.07692307692 + y2 = 0 + 0.07692307692 Reorder the terms: -0.07692307692 + 0.07692307692 + 1.076923077y + y2 = 0 + 0.07692307692 Combine like terms: -0.07692307692 + 0.07692307692 = 0.00000000000 0.00000000000 + 1.076923077y + y2 = 0 + 0.07692307692 1.076923077y + y2 = 0 + 0.07692307692 Combine like terms: 0 + 0.07692307692 = 0.07692307692 1.076923077y + y2 = 0.07692307692 The y term is 1.076923077y. Take half its coefficient (0.5384615385). Square it (0.2899408284) and add it to both sides. Add '0.2899408284' to each side of the equation. 1.076923077y + 0.2899408284 + y2 = 0.07692307692 + 0.2899408284 Reorder the terms: 0.2899408284 + 1.076923077y + y2 = 0.07692307692 + 0.2899408284 Combine like terms: 0.07692307692 + 0.2899408284 = 0.36686390532 0.2899408284 + 1.076923077y + y2 = 0.36686390532 Factor a perfect square on the left side: (y + 0.5384615385)(y + 0.5384615385) = 0.36686390532 Calculate the square root of the right side: 0.605692913 Break this problem into two subproblems by setting (y + 0.5384615385) equal to 0.605692913 and -0.605692913.Subproblem 1
y + 0.5384615385 = 0.605692913 Simplifying y + 0.5384615385 = 0.605692913 Reorder the terms: 0.5384615385 + y = 0.605692913 Solving 0.5384615385 + y = 0.605692913 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5384615385' to each side of the equation. 0.5384615385 + -0.5384615385 + y = 0.605692913 + -0.5384615385 Combine like terms: 0.5384615385 + -0.5384615385 = 0.0000000000 0.0000000000 + y = 0.605692913 + -0.5384615385 y = 0.605692913 + -0.5384615385 Combine like terms: 0.605692913 + -0.5384615385 = 0.0672313745 y = 0.0672313745 Simplifying y = 0.0672313745Subproblem 2
y + 0.5384615385 = -0.605692913 Simplifying y + 0.5384615385 = -0.605692913 Reorder the terms: 0.5384615385 + y = -0.605692913 Solving 0.5384615385 + y = -0.605692913 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5384615385' to each side of the equation. 0.5384615385 + -0.5384615385 + y = -0.605692913 + -0.5384615385 Combine like terms: 0.5384615385 + -0.5384615385 = 0.0000000000 0.0000000000 + y = -0.605692913 + -0.5384615385 y = -0.605692913 + -0.5384615385 Combine like terms: -0.605692913 + -0.5384615385 = -1.1441544515 y = -1.1441544515 Simplifying y = -1.1441544515Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.0672313745, -1.1441544515}
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