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Simplifying x2 + 25x + -15 = 0 Reorder the terms: -15 + 25x + x2 = 0 Solving -15 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 25x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 25x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 25x + x2 = 0 + 15 25x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 25x + x2 = 15 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 15 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 15 + 156.25 Combine like terms: 15 + 156.25 = 171.25 156.25 + 25x + x2 = 171.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 171.25 Calculate the square root of the right side: 13.086252328 Break this problem into two subproblems by setting (x + 12.5) equal to 13.086252328 and -13.086252328.Subproblem 1
x + 12.5 = 13.086252328 Simplifying x + 12.5 = 13.086252328 Reorder the terms: 12.5 + x = 13.086252328 Solving 12.5 + x = 13.086252328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 13.086252328 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 13.086252328 + -12.5 x = 13.086252328 + -12.5 Combine like terms: 13.086252328 + -12.5 = 0.586252328 x = 0.586252328 Simplifying x = 0.586252328Subproblem 2
x + 12.5 = -13.086252328 Simplifying x + 12.5 = -13.086252328 Reorder the terms: 12.5 + x = -13.086252328 Solving 12.5 + x = -13.086252328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -13.086252328 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -13.086252328 + -12.5 x = -13.086252328 + -12.5 Combine like terms: -13.086252328 + -12.5 = -25.586252328 x = -25.586252328 Simplifying x = -25.586252328Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.586252328, -25.586252328}
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