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Simplifying x2 + -35x + 170 = 0 Reorder the terms: 170 + -35x + x2 = 0 Solving 170 + -35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-170' to each side of the equation. 170 + -35x + -170 + x2 = 0 + -170 Reorder the terms: 170 + -170 + -35x + x2 = 0 + -170 Combine like terms: 170 + -170 = 0 0 + -35x + x2 = 0 + -170 -35x + x2 = 0 + -170 Combine like terms: 0 + -170 = -170 -35x + x2 = -170 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 = -170 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -170 + 306.25 Combine like terms: -170 + 306.25 = 136.25 306.25 + -35x + x2 = 136.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 136.25 Calculate the square root of the right side: 11.67261753 Break this problem into two subproblems by setting (x + -17.5) equal to 11.67261753 and -11.67261753.Subproblem 1
x + -17.5 = 11.67261753 Simplifying x + -17.5 = 11.67261753 Reorder the terms: -17.5 + x = 11.67261753 Solving -17.5 + x = 11.67261753 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 = 11.67261753 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 11.67261753 + 17.5 x = 11.67261753 + 17.5 Combine like terms: 11.67261753 + 17.5 = 29.17261753 x = 29.17261753 Simplifying x = 29.17261753Subproblem 2
x + -17.5 = -11.67261753 Simplifying x + -17.5 = -11.67261753 Reorder the terms: -17.5 + x = -11.67261753 Solving -17.5 + x = -11.67261753 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 = -11.67261753 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -11.67261753 + 17.5 x = -11.67261753 + 17.5 Combine like terms: -11.67261753 + 17.5 = 5.82738247 x = 5.82738247 Simplifying x = 5.82738247Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.17261753, 5.82738247}
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