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Simplifying y2 + -19y + -18 = 0 Reorder the terms: -18 + -19y + y2 = 0 Solving -18 + -19y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -19y + 18 + y2 = 0 + 18 Reorder the terms: -18 + 18 + -19y + y2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -19y + y2 = 0 + 18 -19y + y2 = 0 + 18 Combine like terms: 0 + 18 = 18 -19y + y2 = 18 The y term is -19y. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19y + 90.25 + y2 = 18 + 90.25 Reorder the terms: 90.25 + -19y + y2 = 18 + 90.25 Combine like terms: 18 + 90.25 = 108.25 90.25 + -19y + y2 = 108.25 Factor a perfect square on the left side: (y + -9.5)(y + -9.5) = 108.25 Calculate the square root of the right side: 10.404326023 Break this problem into two subproblems by setting (y + -9.5) equal to 10.404326023 and -10.404326023.Subproblem 1
y + -9.5 = 10.404326023 Simplifying y + -9.5 = 10.404326023 Reorder the terms: -9.5 + y = 10.404326023 Solving -9.5 + y = 10.404326023 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = 10.404326023 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = 10.404326023 + 9.5 y = 10.404326023 + 9.5 Combine like terms: 10.404326023 + 9.5 = 19.904326023 y = 19.904326023 Simplifying y = 19.904326023Subproblem 2
y + -9.5 = -10.404326023 Simplifying y + -9.5 = -10.404326023 Reorder the terms: -9.5 + y = -10.404326023 Solving -9.5 + y = -10.404326023 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = -10.404326023 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = -10.404326023 + 9.5 y = -10.404326023 + 9.5 Combine like terms: -10.404326023 + 9.5 = -0.904326023 y = -0.904326023 Simplifying y = -0.904326023Solution
The solution to the problem is based on the solutions from the subproblems. y = {19.904326023, -0.904326023}
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