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Simplifying x2 + -35x + 20 = 0 Reorder the terms: 20 + -35x + x2 = 0 Solving 20 + -35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -35x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -35x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -35x + x2 = 0 + -20 -35x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -35x + x2 = -20 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = -20 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -20 + 306.25 Combine like terms: -20 + 306.25 = 286.25 306.25 + -35x + x2 = 286.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 286.25 Calculate the square root of the right side: 16.918924316 Break this problem into two subproblems by setting (x + -17.5) equal to 16.918924316 and -16.918924316.Subproblem 1
x + -17.5 = 16.918924316 Simplifying x + -17.5 = 16.918924316 Reorder the terms: -17.5 + x = 16.918924316 Solving -17.5 + x = 16.918924316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 16.918924316 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 16.918924316 + 17.5 x = 16.918924316 + 17.5 Combine like terms: 16.918924316 + 17.5 = 34.418924316 x = 34.418924316 Simplifying x = 34.418924316Subproblem 2
x + -17.5 = -16.918924316 Simplifying x + -17.5 = -16.918924316 Reorder the terms: -17.5 + x = -16.918924316 Solving -17.5 + x = -16.918924316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -16.918924316 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -16.918924316 + 17.5 x = -16.918924316 + 17.5 Combine like terms: -16.918924316 + 17.5 = 0.581075684 x = 0.581075684 Simplifying x = 0.581075684Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.418924316, 0.581075684}
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