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Simplifying x2 + -19x + -40 = 0 Reorder the terms: -40 + -19x + x2 = 0 Solving -40 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -19x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -19x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -19x + x2 = 0 + 40 -19x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -19x + x2 = 40 The x term is -19x. 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. -19x + 90.25 + x2 = 40 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 40 + 90.25 Combine like terms: 40 + 90.25 = 130.25 90.25 + -19x + x2 = 130.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (x + -9.5) equal to 11.412712211 and -11.412712211.Subproblem 1
x + -9.5 = 11.412712211 Simplifying x + -9.5 = 11.412712211 Reorder the terms: -9.5 + x = 11.412712211 Solving -9.5 + x = 11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 11.412712211 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 11.412712211 + 9.5 x = 11.412712211 + 9.5 Combine like terms: 11.412712211 + 9.5 = 20.912712211 x = 20.912712211 Simplifying x = 20.912712211Subproblem 2
x + -9.5 = -11.412712211 Simplifying x + -9.5 = -11.412712211 Reorder the terms: -9.5 + x = -11.412712211 Solving -9.5 + x = -11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -11.412712211 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -11.412712211 + 9.5 x = -11.412712211 + 9.5 Combine like terms: -11.412712211 + 9.5 = -1.912712211 x = -1.912712211 Simplifying x = -1.912712211Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.912712211, -1.912712211}
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