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Simplifying 2x2 + -38x + 5 = 0 Reorder the terms: 5 + -38x + 2x2 = 0 Solving 5 + -38x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -19x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -19x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -19x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -19x + x2 = 0 + -2.5 -19x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -19x + x2 = -2.5 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 = -2.5 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -2.5 + 90.25 Combine like terms: -2.5 + 90.25 = 87.75 90.25 + -19x + x2 = 87.75 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 87.75 Calculate the square root of the right side: 9.367496998 Break this problem into two subproblems by setting (x + -9.5) equal to 9.367496998 and -9.367496998.Subproblem 1
x + -9.5 = 9.367496998 Simplifying x + -9.5 = 9.367496998 Reorder the terms: -9.5 + x = 9.367496998 Solving -9.5 + x = 9.367496998 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 = 9.367496998 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 9.367496998 + 9.5 x = 9.367496998 + 9.5 Combine like terms: 9.367496998 + 9.5 = 18.867496998 x = 18.867496998 Simplifying x = 18.867496998Subproblem 2
x + -9.5 = -9.367496998 Simplifying x + -9.5 = -9.367496998 Reorder the terms: -9.5 + x = -9.367496998 Solving -9.5 + x = -9.367496998 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 = -9.367496998 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -9.367496998 + 9.5 x = -9.367496998 + 9.5 Combine like terms: -9.367496998 + 9.5 = 0.132503002 x = 0.132503002 Simplifying x = 0.132503002Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.867496998, 0.132503002}
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