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Simplifying x2 + -19x + 50 = 0 Reorder the terms: 50 + -19x + x2 = 0 Solving 50 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -19x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -19x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -19x + x2 = 0 + -50 -19x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -19x + x2 = -50 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 = -50 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -50 + 90.25 Combine like terms: -50 + 90.25 = 40.25 90.25 + -19x + x2 = 40.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + -9.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + -9.5 = 6.34428877 Simplifying x + -9.5 = 6.34428877 Reorder the terms: -9.5 + x = 6.34428877 Solving -9.5 + x = 6.34428877 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 = 6.34428877 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 6.34428877 + 9.5 x = 6.34428877 + 9.5 Combine like terms: 6.34428877 + 9.5 = 15.84428877 x = 15.84428877 Simplifying x = 15.84428877Subproblem 2
x + -9.5 = -6.34428877 Simplifying x + -9.5 = -6.34428877 Reorder the terms: -9.5 + x = -6.34428877 Solving -9.5 + x = -6.34428877 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 = -6.34428877 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -6.34428877 + 9.5 x = -6.34428877 + 9.5 Combine like terms: -6.34428877 + 9.5 = 3.15571123 x = 3.15571123 Simplifying x = 3.15571123Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.84428877, 3.15571123}
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