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Simplifying 7y2 + 13y + -1 = 11y Reorder the terms: -1 + 13y + 7y2 = 11y Solving -1 + 13y + 7y2 = 11y Solving for variable 'y'. Reorder the terms: -1 + 13y + -11y + 7y2 = 11y + -11y Combine like terms: 13y + -11y = 2y -1 + 2y + 7y2 = 11y + -11y Combine like terms: 11y + -11y = 0 -1 + 2y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + 0.2857142857y + y2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.2857142857y + 0.1428571429 + y2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + 0.2857142857y + y2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + 0.2857142857y + y2 = 0 + 0.1428571429 0.2857142857y + y2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 0.2857142857y + y2 = 0.1428571429 The y term is 0.2857142857y. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857y + 0.02040816328 + y2 = 0.1428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857y + y2 = 0.1428571429 + 0.02040816328 Combine like terms: 0.1428571429 + 0.02040816328 = 0.16326530618 0.02040816328 + 0.2857142857y + y2 = 0.16326530618 Factor a perfect square on the left side: (y + 0.1428571429)(y + 0.1428571429) = 0.16326530618 Calculate the square root of the right side: 0.404061018 Break this problem into two subproblems by setting (y + 0.1428571429) equal to 0.404061018 and -0.404061018.Subproblem 1
y + 0.1428571429 = 0.404061018 Simplifying y + 0.1428571429 = 0.404061018 Reorder the terms: 0.1428571429 + y = 0.404061018 Solving 0.1428571429 + y = 0.404061018 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + y = 0.404061018 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + y = 0.404061018 + -0.1428571429 y = 0.404061018 + -0.1428571429 Combine like terms: 0.404061018 + -0.1428571429 = 0.2612038751 y = 0.2612038751 Simplifying y = 0.2612038751Subproblem 2
y + 0.1428571429 = -0.404061018 Simplifying y + 0.1428571429 = -0.404061018 Reorder the terms: 0.1428571429 + y = -0.404061018 Solving 0.1428571429 + y = -0.404061018 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + y = -0.404061018 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + y = -0.404061018 + -0.1428571429 y = -0.404061018 + -0.1428571429 Combine like terms: -0.404061018 + -0.1428571429 = -0.5469181609 y = -0.5469181609 Simplifying y = -0.5469181609Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.2612038751, -0.5469181609}
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