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Simplifying x2 + -19x + 8 = 0 Reorder the terms: 8 + -19x + x2 = 0 Solving 8 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -19x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -19x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -19x + x2 = 0 + -8 -19x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -19x + x2 = -8 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 = -8 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -8 + 90.25 Combine like terms: -8 + 90.25 = 82.25 90.25 + -19x + x2 = 82.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (x + -9.5) equal to 9.069178574 and -9.069178574.Subproblem 1
x + -9.5 = 9.069178574 Simplifying x + -9.5 = 9.069178574 Reorder the terms: -9.5 + x = 9.069178574 Solving -9.5 + x = 9.069178574 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 = 9.069178574 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 9.069178574 + 9.5 x = 9.069178574 + 9.5 Combine like terms: 9.069178574 + 9.5 = 18.569178574 x = 18.569178574 Simplifying x = 18.569178574Subproblem 2
x + -9.5 = -9.069178574 Simplifying x + -9.5 = -9.069178574 Reorder the terms: -9.5 + x = -9.069178574 Solving -9.5 + x = -9.069178574 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 = -9.069178574 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -9.069178574 + 9.5 x = -9.069178574 + 9.5 Combine like terms: -9.069178574 + 9.5 = 0.430821426 x = 0.430821426 Simplifying x = 0.430821426Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.569178574, 0.430821426}
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