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Simplifying x2 + -20x + 37.5 = 0 Reorder the terms: 37.5 + -20x + x2 = 0 Solving 37.5 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-37.5' to each side of the equation. 37.5 + -20x + -37.5 + x2 = 0 + -37.5 Reorder the terms: 37.5 + -37.5 + -20x + x2 = 0 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + -20x + x2 = 0 + -37.5 -20x + x2 = 0 + -37.5 Combine like terms: 0 + -37.5 = -37.5 -20x + x2 = -37.5 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -37.5 + 100 Reorder the terms: 100 + -20x + x2 = -37.5 + 100 Combine like terms: -37.5 + 100 = 62.5 100 + -20x + x2 = 62.5 Factor a perfect square on the left side: (x + -10)(x + -10) = 62.5 Calculate the square root of the right side: 7.90569415 Break this problem into two subproblems by setting (x + -10) equal to 7.90569415 and -7.90569415.Subproblem 1
x + -10 = 7.90569415 Simplifying x + -10 = 7.90569415 Reorder the terms: -10 + x = 7.90569415 Solving -10 + x = 7.90569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 7.90569415 + 10 Combine like terms: -10 + 10 = 0 0 + x = 7.90569415 + 10 x = 7.90569415 + 10 Combine like terms: 7.90569415 + 10 = 17.90569415 x = 17.90569415 Simplifying x = 17.90569415Subproblem 2
x + -10 = -7.90569415 Simplifying x + -10 = -7.90569415 Reorder the terms: -10 + x = -7.90569415 Solving -10 + x = -7.90569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -7.90569415 + 10 Combine like terms: -10 + 10 = 0 0 + x = -7.90569415 + 10 x = -7.90569415 + 10 Combine like terms: -7.90569415 + 10 = 2.09430585 x = 2.09430585 Simplifying x = 2.09430585Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.90569415, 2.09430585}
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