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Simplifying 31y2 + -226y + 203 = 0 Reorder the terms: 203 + -226y + 31y2 = 0 Solving 203 + -226y + 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'. 6.548387097 + -7.290322581y + y2 = 0 Move the constant term to the right: Add '-6.548387097' to each side of the equation. 6.548387097 + -7.290322581y + -6.548387097 + y2 = 0 + -6.548387097 Reorder the terms: 6.548387097 + -6.548387097 + -7.290322581y + y2 = 0 + -6.548387097 Combine like terms: 6.548387097 + -6.548387097 = 0.000000000 0.000000000 + -7.290322581y + y2 = 0 + -6.548387097 -7.290322581y + y2 = 0 + -6.548387097 Combine like terms: 0 + -6.548387097 = -6.548387097 -7.290322581y + y2 = -6.548387097 The y term is -7.290322581y. Take half its coefficient (-3.645161291). Square it (13.28720084) and add it to both sides. Add '13.28720084' to each side of the equation. -7.290322581y + 13.28720084 + y2 = -6.548387097 + 13.28720084 Reorder the terms: 13.28720084 + -7.290322581y + y2 = -6.548387097 + 13.28720084 Combine like terms: -6.548387097 + 13.28720084 = 6.738813743 13.28720084 + -7.290322581y + y2 = 6.738813743 Factor a perfect square on the left side: (y + -3.645161291)(y + -3.645161291) = 6.738813743 Calculate the square root of the right side: 2.595922523 Break this problem into two subproblems by setting (y + -3.645161291) equal to 2.595922523 and -2.595922523.Subproblem 1
y + -3.645161291 = 2.595922523 Simplifying y + -3.645161291 = 2.595922523 Reorder the terms: -3.645161291 + y = 2.595922523 Solving -3.645161291 + y = 2.595922523 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.645161291' to each side of the equation. -3.645161291 + 3.645161291 + y = 2.595922523 + 3.645161291 Combine like terms: -3.645161291 + 3.645161291 = 0.000000000 0.000000000 + y = 2.595922523 + 3.645161291 y = 2.595922523 + 3.645161291 Combine like terms: 2.595922523 + 3.645161291 = 6.241083814 y = 6.241083814 Simplifying y = 6.241083814Subproblem 2
y + -3.645161291 = -2.595922523 Simplifying y + -3.645161291 = -2.595922523 Reorder the terms: -3.645161291 + y = -2.595922523 Solving -3.645161291 + y = -2.595922523 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.645161291' to each side of the equation. -3.645161291 + 3.645161291 + y = -2.595922523 + 3.645161291 Combine like terms: -3.645161291 + 3.645161291 = 0.000000000 0.000000000 + y = -2.595922523 + 3.645161291 y = -2.595922523 + 3.645161291 Combine like terms: -2.595922523 + 3.645161291 = 1.049238768 y = 1.049238768 Simplifying y = 1.049238768Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.241083814, 1.049238768}
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