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Simplifying x2 + -35x + 5 = 0 Reorder the terms: 5 + -35x + x2 = 0 Solving 5 + -35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -35x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -35x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -35x + x2 = 0 + -5 -35x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -35x + x2 = -5 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 = -5 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -5 + 306.25 Combine like terms: -5 + 306.25 = 301.25 306.25 + -35x + x2 = 301.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 301.25 Calculate the square root of the right side: 17.356554958 Break this problem into two subproblems by setting (x + -17.5) equal to 17.356554958 and -17.356554958.Subproblem 1
x + -17.5 = 17.356554958 Simplifying x + -17.5 = 17.356554958 Reorder the terms: -17.5 + x = 17.356554958 Solving -17.5 + x = 17.356554958 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 = 17.356554958 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 17.356554958 + 17.5 x = 17.356554958 + 17.5 Combine like terms: 17.356554958 + 17.5 = 34.856554958 x = 34.856554958 Simplifying x = 34.856554958Subproblem 2
x + -17.5 = -17.356554958 Simplifying x + -17.5 = -17.356554958 Reorder the terms: -17.5 + x = -17.356554958 Solving -17.5 + x = -17.356554958 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 = -17.356554958 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -17.356554958 + 17.5 x = -17.356554958 + 17.5 Combine like terms: -17.356554958 + 17.5 = 0.143445042 x = 0.143445042 Simplifying x = 0.143445042Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.856554958, 0.143445042}
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