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Simplifying x2 + -114x + 399 = 0 Reorder the terms: 399 + -114x + x2 = 0 Solving 399 + -114x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-399' to each side of the equation. 399 + -114x + -399 + x2 = 0 + -399 Reorder the terms: 399 + -399 + -114x + x2 = 0 + -399 Combine like terms: 399 + -399 = 0 0 + -114x + x2 = 0 + -399 -114x + x2 = 0 + -399 Combine like terms: 0 + -399 = -399 -114x + x2 = -399 The x term is -114x. Take half its coefficient (-57). Square it (3249) and add it to both sides. Add '3249' to each side of the equation. -114x + 3249 + x2 = -399 + 3249 Reorder the terms: 3249 + -114x + x2 = -399 + 3249 Combine like terms: -399 + 3249 = 2850 3249 + -114x + x2 = 2850 Factor a perfect square on the left side: (x + -57)(x + -57) = 2850 Calculate the square root of the right side: 53.38539126 Break this problem into two subproblems by setting (x + -57) equal to 53.38539126 and -53.38539126.Subproblem 1
x + -57 = 53.38539126 Simplifying x + -57 = 53.38539126 Reorder the terms: -57 + x = 53.38539126 Solving -57 + x = 53.38539126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '57' to each side of the equation. -57 + 57 + x = 53.38539126 + 57 Combine like terms: -57 + 57 = 0 0 + x = 53.38539126 + 57 x = 53.38539126 + 57 Combine like terms: 53.38539126 + 57 = 110.38539126 x = 110.38539126 Simplifying x = 110.38539126Subproblem 2
x + -57 = -53.38539126 Simplifying x + -57 = -53.38539126 Reorder the terms: -57 + x = -53.38539126 Solving -57 + x = -53.38539126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '57' to each side of the equation. -57 + 57 + x = -53.38539126 + 57 Combine like terms: -57 + 57 = 0 0 + x = -53.38539126 + 57 x = -53.38539126 + 57 Combine like terms: -53.38539126 + 57 = 3.61460874 x = 3.61460874 Simplifying x = 3.61460874Solution
The solution to the problem is based on the solutions from the subproblems. x = {110.38539126, 3.61460874}
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