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Simplifying x2 + 25x + 125 = 0 Reorder the terms: 125 + 25x + x2 = 0 Solving 125 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-125' to each side of the equation. 125 + 25x + -125 + x2 = 0 + -125 Reorder the terms: 125 + -125 + 25x + x2 = 0 + -125 Combine like terms: 125 + -125 = 0 0 + 25x + x2 = 0 + -125 25x + x2 = 0 + -125 Combine like terms: 0 + -125 = -125 25x + x2 = -125 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 = -125 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -125 + 156.25 Combine like terms: -125 + 156.25 = 31.25 156.25 + 25x + x2 = 31.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x + 12.5) equal to 5.590169944 and -5.590169944.Subproblem 1
x + 12.5 = 5.590169944 Simplifying x + 12.5 = 5.590169944 Reorder the terms: 12.5 + x = 5.590169944 Solving 12.5 + x = 5.590169944 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 = 5.590169944 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 5.590169944 + -12.5 x = 5.590169944 + -12.5 Combine like terms: 5.590169944 + -12.5 = -6.909830056 x = -6.909830056 Simplifying x = -6.909830056Subproblem 2
x + 12.5 = -5.590169944 Simplifying x + 12.5 = -5.590169944 Reorder the terms: 12.5 + x = -5.590169944 Solving 12.5 + x = -5.590169944 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 = -5.590169944 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -5.590169944 + -12.5 x = -5.590169944 + -12.5 Combine like terms: -5.590169944 + -12.5 = -18.090169944 x = -18.090169944 Simplifying x = -18.090169944Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.909830056, -18.090169944}
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