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Simplifying x2 + -35x + 36 = 0 Reorder the terms: 36 + -35x + x2 = 0 Solving 36 + -35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -35x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -35x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -35x + x2 = 0 + -36 -35x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -35x + x2 = -36 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 = -36 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -36 + 306.25 Combine like terms: -36 + 306.25 = 270.25 306.25 + -35x + x2 = 270.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 270.25 Calculate the square root of the right side: 16.439282223 Break this problem into two subproblems by setting (x + -17.5) equal to 16.439282223 and -16.439282223.Subproblem 1
x + -17.5 = 16.439282223 Simplifying x + -17.5 = 16.439282223 Reorder the terms: -17.5 + x = 16.439282223 Solving -17.5 + x = 16.439282223 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 = 16.439282223 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 16.439282223 + 17.5 x = 16.439282223 + 17.5 Combine like terms: 16.439282223 + 17.5 = 33.939282223 x = 33.939282223 Simplifying x = 33.939282223Subproblem 2
x + -17.5 = -16.439282223 Simplifying x + -17.5 = -16.439282223 Reorder the terms: -17.5 + x = -16.439282223 Solving -17.5 + x = -16.439282223 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 = -16.439282223 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -16.439282223 + 17.5 x = -16.439282223 + 17.5 Combine like terms: -16.439282223 + 17.5 = 1.060717777 x = 1.060717777 Simplifying x = 1.060717777Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.939282223, 1.060717777}
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