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Simplifying x2 + -55x + -500 = 0 Reorder the terms: -500 + -55x + x2 = 0 Solving -500 + -55x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + -55x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + -55x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + -55x + x2 = 0 + 500 -55x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 -55x + x2 = 500 The x term is -55x. Take half its coefficient (-27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. -55x + 756.25 + x2 = 500 + 756.25 Reorder the terms: 756.25 + -55x + x2 = 500 + 756.25 Combine like terms: 500 + 756.25 = 1256.25 756.25 + -55x + x2 = 1256.25 Factor a perfect square on the left side: (x + -27.5)(x + -27.5) = 1256.25 Calculate the square root of the right side: 35.443617197 Break this problem into two subproblems by setting (x + -27.5) equal to 35.443617197 and -35.443617197.Subproblem 1
x + -27.5 = 35.443617197 Simplifying x + -27.5 = 35.443617197 Reorder the terms: -27.5 + x = 35.443617197 Solving -27.5 + x = 35.443617197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = 35.443617197 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = 35.443617197 + 27.5 x = 35.443617197 + 27.5 Combine like terms: 35.443617197 + 27.5 = 62.943617197 x = 62.943617197 Simplifying x = 62.943617197Subproblem 2
x + -27.5 = -35.443617197 Simplifying x + -27.5 = -35.443617197 Reorder the terms: -27.5 + x = -35.443617197 Solving -27.5 + x = -35.443617197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = -35.443617197 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = -35.443617197 + 27.5 x = -35.443617197 + 27.5 Combine like terms: -35.443617197 + 27.5 = -7.943617197 x = -7.943617197 Simplifying x = -7.943617197Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.943617197, -7.943617197}
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