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Simplifying 1y + 5 + -5y + -5 = 14y2 + -25 Reorder the terms: 5 + -5 + 1y + -5y = 14y2 + -25 Combine like terms: 5 + -5 = 0 0 + 1y + -5y = 14y2 + -25 1y + -5y = 14y2 + -25 Combine like terms: 1y + -5y = -4y -4y = 14y2 + -25 Reorder the terms: -4y = -25 + 14y2 Solving -4y = -25 + 14y2 Solving for variable 'y'. Reorder the terms: 25 + -4y + -14y2 = -25 + 14y2 + 25 + -14y2 Reorder the terms: 25 + -4y + -14y2 = -25 + 25 + 14y2 + -14y2 Combine like terms: -25 + 25 = 0 25 + -4y + -14y2 = 0 + 14y2 + -14y2 25 + -4y + -14y2 = 14y2 + -14y2 Combine like terms: 14y2 + -14y2 = 0 25 + -4y + -14y2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -1.785714286 + 0.2857142857y + y2 = 0 Move the constant term to the right: Add '1.785714286' to each side of the equation. -1.785714286 + 0.2857142857y + 1.785714286 + y2 = 0 + 1.785714286 Reorder the terms: -1.785714286 + 1.785714286 + 0.2857142857y + y2 = 0 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + 0.2857142857y + y2 = 0 + 1.785714286 0.2857142857y + y2 = 0 + 1.785714286 Combine like terms: 0 + 1.785714286 = 1.785714286 0.2857142857y + y2 = 1.785714286 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 = 1.785714286 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857y + y2 = 1.785714286 + 0.02040816328 Combine like terms: 1.785714286 + 0.02040816328 = 1.80612244928 0.02040816328 + 0.2857142857y + y2 = 1.80612244928 Factor a perfect square on the left side: (y + 0.1428571429)(y + 0.1428571429) = 1.80612244928 Calculate the square root of the right side: 1.343920552 Break this problem into two subproblems by setting (y + 0.1428571429) equal to 1.343920552 and -1.343920552.Subproblem 1
y + 0.1428571429 = 1.343920552 Simplifying y + 0.1428571429 = 1.343920552 Reorder the terms: 0.1428571429 + y = 1.343920552 Solving 0.1428571429 + y = 1.343920552 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 = 1.343920552 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + y = 1.343920552 + -0.1428571429 y = 1.343920552 + -0.1428571429 Combine like terms: 1.343920552 + -0.1428571429 = 1.2010634091 y = 1.2010634091 Simplifying y = 1.2010634091Subproblem 2
y + 0.1428571429 = -1.343920552 Simplifying y + 0.1428571429 = -1.343920552 Reorder the terms: 0.1428571429 + y = -1.343920552 Solving 0.1428571429 + y = -1.343920552 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 = -1.343920552 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + y = -1.343920552 + -0.1428571429 y = -1.343920552 + -0.1428571429 Combine like terms: -1.343920552 + -0.1428571429 = -1.4867776949 y = -1.4867776949 Simplifying y = -1.4867776949Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.2010634091, -1.4867776949}
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