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Simplifying x2 + 5x + -125 = 0 Reorder the terms: -125 + 5x + x2 = 0 Solving -125 + 5x + 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 + 5x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + 5x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 5x + x2 = 0 + 125 5x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 5x + x2 = 125 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 125 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 125 + 6.25 Combine like terms: 125 + 6.25 = 131.25 6.25 + 5x + x2 = 131.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 131.25 Calculate the square root of the right side: 11.456439237 Break this problem into two subproblems by setting (x + 2.5) equal to 11.456439237 and -11.456439237.Subproblem 1
x + 2.5 = 11.456439237 Simplifying x + 2.5 = 11.456439237 Reorder the terms: 2.5 + x = 11.456439237 Solving 2.5 + x = 11.456439237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 11.456439237 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 11.456439237 + -2.5 x = 11.456439237 + -2.5 Combine like terms: 11.456439237 + -2.5 = 8.956439237 x = 8.956439237 Simplifying x = 8.956439237Subproblem 2
x + 2.5 = -11.456439237 Simplifying x + 2.5 = -11.456439237 Reorder the terms: 2.5 + x = -11.456439237 Solving 2.5 + x = -11.456439237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -11.456439237 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -11.456439237 + -2.5 x = -11.456439237 + -2.5 Combine like terms: -11.456439237 + -2.5 = -13.956439237 x = -13.956439237 Simplifying x = -13.956439237Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.956439237, -13.956439237}
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