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Simplifying x2 + -10x + -37.5 = 0 Reorder the terms: -37.5 + -10x + x2 = 0 Solving -37.5 + -10x + 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 + -10x + 37.5 + x2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + -10x + x2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + -10x + x2 = 0 + 37.5 -10x + x2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 -10x + x2 = 37.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 37.5 + 25 Reorder the terms: 25 + -10x + x2 = 37.5 + 25 Combine like terms: 37.5 + 25 = 62.5 25 + -10x + x2 = 62.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 62.5 Calculate the square root of the right side: 7.90569415 Break this problem into two subproblems by setting (x + -5) equal to 7.90569415 and -7.90569415.Subproblem 1
x + -5 = 7.90569415 Simplifying x + -5 = 7.90569415 Reorder the terms: -5 + x = 7.90569415 Solving -5 + x = 7.90569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 7.90569415 + 5 Combine like terms: -5 + 5 = 0 0 + x = 7.90569415 + 5 x = 7.90569415 + 5 Combine like terms: 7.90569415 + 5 = 12.90569415 x = 12.90569415 Simplifying x = 12.90569415Subproblem 2
x + -5 = -7.90569415 Simplifying x + -5 = -7.90569415 Reorder the terms: -5 + x = -7.90569415 Solving -5 + x = -7.90569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -7.90569415 + 5 Combine like terms: -5 + 5 = 0 0 + x = -7.90569415 + 5 x = -7.90569415 + 5 Combine like terms: -7.90569415 + 5 = -2.90569415 x = -2.90569415 Simplifying x = -2.90569415Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.90569415, -2.90569415}
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