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Simplifying 31y2 + 8y + -7 = 0 Reorder the terms: -7 + 8y + 31y2 = 0 Solving -7 + 8y + 31y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 31 the coefficient of the squared term: Divide each side by '31'. -0.2258064516 + 0.2580645161y + y2 = 0 Move the constant term to the right: Add '0.2258064516' to each side of the equation. -0.2258064516 + 0.2580645161y + 0.2258064516 + y2 = 0 + 0.2258064516 Reorder the terms: -0.2258064516 + 0.2258064516 + 0.2580645161y + y2 = 0 + 0.2258064516 Combine like terms: -0.2258064516 + 0.2258064516 = 0.0000000000 0.0000000000 + 0.2580645161y + y2 = 0 + 0.2258064516 0.2580645161y + y2 = 0 + 0.2258064516 Combine like terms: 0 + 0.2258064516 = 0.2258064516 0.2580645161y + y2 = 0.2258064516 The y term is 0.2580645161y. Take half its coefficient (0.1290322581). Square it (0.01664932363) and add it to both sides. Add '0.01664932363' to each side of the equation. 0.2580645161y + 0.01664932363 + y2 = 0.2258064516 + 0.01664932363 Reorder the terms: 0.01664932363 + 0.2580645161y + y2 = 0.2258064516 + 0.01664932363 Combine like terms: 0.2258064516 + 0.01664932363 = 0.24245577523 0.01664932363 + 0.2580645161y + y2 = 0.24245577523 Factor a perfect square on the left side: (y + 0.1290322581)(y + 0.1290322581) = 0.24245577523 Calculate the square root of the right side: 0.492397985 Break this problem into two subproblems by setting (y + 0.1290322581) equal to 0.492397985 and -0.492397985.Subproblem 1
y + 0.1290322581 = 0.492397985 Simplifying y + 0.1290322581 = 0.492397985 Reorder the terms: 0.1290322581 + y = 0.492397985 Solving 0.1290322581 + y = 0.492397985 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1290322581' to each side of the equation. 0.1290322581 + -0.1290322581 + y = 0.492397985 + -0.1290322581 Combine like terms: 0.1290322581 + -0.1290322581 = 0.0000000000 0.0000000000 + y = 0.492397985 + -0.1290322581 y = 0.492397985 + -0.1290322581 Combine like terms: 0.492397985 + -0.1290322581 = 0.3633657269 y = 0.3633657269 Simplifying y = 0.3633657269Subproblem 2
y + 0.1290322581 = -0.492397985 Simplifying y + 0.1290322581 = -0.492397985 Reorder the terms: 0.1290322581 + y = -0.492397985 Solving 0.1290322581 + y = -0.492397985 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1290322581' to each side of the equation. 0.1290322581 + -0.1290322581 + y = -0.492397985 + -0.1290322581 Combine like terms: 0.1290322581 + -0.1290322581 = 0.0000000000 0.0000000000 + y = -0.492397985 + -0.1290322581 y = -0.492397985 + -0.1290322581 Combine like terms: -0.492397985 + -0.1290322581 = -0.6214302431 y = -0.6214302431 Simplifying y = -0.6214302431Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.3633657269, -0.6214302431}
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