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Simplifying x2 + -1x = 250 Reorder the terms: -1x + x2 = 250 Solving -1x + x2 = 250 Solving for variable 'x'. Reorder the terms: -250 + -1x + x2 = 250 + -250 Combine like terms: 250 + -250 = 0 -250 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + -1x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + -1x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + -1x + x2 = 0 + 250 -1x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 -1x + x2 = 250 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 250 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 250 + 0.25 Combine like terms: 250 + 0.25 = 250.25 0.25 + -1x + x2 = 250.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 250.25 Calculate the square root of the right side: 15.81929202 Break this problem into two subproblems by setting (x + -0.5) equal to 15.81929202 and -15.81929202.Subproblem 1
x + -0.5 = 15.81929202 Simplifying x + -0.5 = 15.81929202 Reorder the terms: -0.5 + x = 15.81929202 Solving -0.5 + x = 15.81929202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 15.81929202 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 15.81929202 + 0.5 x = 15.81929202 + 0.5 Combine like terms: 15.81929202 + 0.5 = 16.31929202 x = 16.31929202 Simplifying x = 16.31929202Subproblem 2
x + -0.5 = -15.81929202 Simplifying x + -0.5 = -15.81929202 Reorder the terms: -0.5 + x = -15.81929202 Solving -0.5 + x = -15.81929202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -15.81929202 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -15.81929202 + 0.5 x = -15.81929202 + 0.5 Combine like terms: -15.81929202 + 0.5 = -15.31929202 x = -15.31929202 Simplifying x = -15.31929202Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.31929202, -15.31929202}
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