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Simplifying y2 + -11y = -26 Reorder the terms: -11y + y2 = -26 Solving -11y + y2 = -26 Solving for variable 'y'. Reorder the terms: 26 + -11y + y2 = -26 + 26 Combine like terms: -26 + 26 = 0 26 + -11y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + -11y + -26 + y2 = 0 + -26 Reorder the terms: 26 + -26 + -11y + y2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -11y + y2 = 0 + -26 -11y + y2 = 0 + -26 Combine like terms: 0 + -26 = -26 -11y + y2 = -26 The y term is -11y. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11y + 30.25 + y2 = -26 + 30.25 Reorder the terms: 30.25 + -11y + y2 = -26 + 30.25 Combine like terms: -26 + 30.25 = 4.25 30.25 + -11y + y2 = 4.25 Factor a perfect square on the left side: (y + -5.5)(y + -5.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (y + -5.5) equal to 2.061552813 and -2.061552813.Subproblem 1
y + -5.5 = 2.061552813 Simplifying y + -5.5 = 2.061552813 Reorder the terms: -5.5 + y = 2.061552813 Solving -5.5 + y = 2.061552813 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = 2.061552813 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = 2.061552813 + 5.5 y = 2.061552813 + 5.5 Combine like terms: 2.061552813 + 5.5 = 7.561552813 y = 7.561552813 Simplifying y = 7.561552813Subproblem 2
y + -5.5 = -2.061552813 Simplifying y + -5.5 = -2.061552813 Reorder the terms: -5.5 + y = -2.061552813 Solving -5.5 + y = -2.061552813 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = -2.061552813 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = -2.061552813 + 5.5 y = -2.061552813 + 5.5 Combine like terms: -2.061552813 + 5.5 = 3.438447187 y = 3.438447187 Simplifying y = 3.438447187Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.561552813, 3.438447187}
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