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Simplifying 5y2 + -26y + 31 = 0 Reorder the terms: 31 + -26y + 5y2 = 0 Solving 31 + -26y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 6.2 + -5.2y + y2 = 0 Move the constant term to the right: Add '-6.2' to each side of the equation. 6.2 + -5.2y + -6.2 + y2 = 0 + -6.2 Reorder the terms: 6.2 + -6.2 + -5.2y + y2 = 0 + -6.2 Combine like terms: 6.2 + -6.2 = 0.0 0.0 + -5.2y + y2 = 0 + -6.2 -5.2y + y2 = 0 + -6.2 Combine like terms: 0 + -6.2 = -6.2 -5.2y + y2 = -6.2 The y term is -5.2y. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2y + 6.76 + y2 = -6.2 + 6.76 Reorder the terms: 6.76 + -5.2y + y2 = -6.2 + 6.76 Combine like terms: -6.2 + 6.76 = 0.56 6.76 + -5.2y + y2 = 0.56 Factor a perfect square on the left side: (y + -2.6)(y + -2.6) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (y + -2.6) equal to 0.748331477 and -0.748331477.Subproblem 1
y + -2.6 = 0.748331477 Simplifying y + -2.6 = 0.748331477 Reorder the terms: -2.6 + y = 0.748331477 Solving -2.6 + y = 0.748331477 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + y = 0.748331477 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + y = 0.748331477 + 2.6 y = 0.748331477 + 2.6 Combine like terms: 0.748331477 + 2.6 = 3.348331477 y = 3.348331477 Simplifying y = 3.348331477Subproblem 2
y + -2.6 = -0.748331477 Simplifying y + -2.6 = -0.748331477 Reorder the terms: -2.6 + y = -0.748331477 Solving -2.6 + y = -0.748331477 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + y = -0.748331477 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + y = -0.748331477 + 2.6 y = -0.748331477 + 2.6 Combine like terms: -0.748331477 + 2.6 = 1.851668523 y = 1.851668523 Simplifying y = 1.851668523Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.348331477, 1.851668523}
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