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Simplifying x2 + -35x = 190 Reorder the terms: -35x + x2 = 190 Solving -35x + x2 = 190 Solving for variable 'x'. Reorder the terms: -190 + -35x + x2 = 190 + -190 Combine like terms: 190 + -190 = 0 -190 + -35x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '190' to each side of the equation. -190 + -35x + 190 + x2 = 0 + 190 Reorder the terms: -190 + 190 + -35x + x2 = 0 + 190 Combine like terms: -190 + 190 = 0 0 + -35x + x2 = 0 + 190 -35x + x2 = 0 + 190 Combine like terms: 0 + 190 = 190 -35x + x2 = 190 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 = 190 + 306.25 Reorder the terms: 306.25 + -35x + x2 = 190 + 306.25 Combine like terms: 190 + 306.25 = 496.25 306.25 + -35x + x2 = 496.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 496.25 Calculate the square root of the right side: 22.27666941 Break this problem into two subproblems by setting (x + -17.5) equal to 22.27666941 and -22.27666941.Subproblem 1
x + -17.5 = 22.27666941 Simplifying x + -17.5 = 22.27666941 Reorder the terms: -17.5 + x = 22.27666941 Solving -17.5 + x = 22.27666941 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 = 22.27666941 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 22.27666941 + 17.5 x = 22.27666941 + 17.5 Combine like terms: 22.27666941 + 17.5 = 39.77666941 x = 39.77666941 Simplifying x = 39.77666941Subproblem 2
x + -17.5 = -22.27666941 Simplifying x + -17.5 = -22.27666941 Reorder the terms: -17.5 + x = -22.27666941 Solving -17.5 + x = -22.27666941 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 = -22.27666941 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -22.27666941 + 17.5 x = -22.27666941 + 17.5 Combine like terms: -22.27666941 + 17.5 = -4.77666941 x = -4.77666941 Simplifying x = -4.77666941Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.77666941, -4.77666941}
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