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Simplifying x2 + 25x + 25 = 0 Reorder the terms: 25 + 25x + x2 = 0 Solving 25 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 25x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + 25x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 25x + x2 = 0 + -25 25x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 25x + x2 = -25 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 = -25 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -25 + 156.25 Combine like terms: -25 + 156.25 = 131.25 156.25 + 25x + x2 = 131.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 131.25 Calculate the square root of the right side: 11.456439237 Break this problem into two subproblems by setting (x + 12.5) equal to 11.456439237 and -11.456439237.Subproblem 1
x + 12.5 = 11.456439237 Simplifying x + 12.5 = 11.456439237 Reorder the terms: 12.5 + x = 11.456439237 Solving 12.5 + x = 11.456439237 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 = 11.456439237 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 11.456439237 + -12.5 x = 11.456439237 + -12.5 Combine like terms: 11.456439237 + -12.5 = -1.043560763 x = -1.043560763 Simplifying x = -1.043560763Subproblem 2
x + 12.5 = -11.456439237 Simplifying x + 12.5 = -11.456439237 Reorder the terms: 12.5 + x = -11.456439237 Solving 12.5 + x = -11.456439237 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 = -11.456439237 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -11.456439237 + -12.5 x = -11.456439237 + -12.5 Combine like terms: -11.456439237 + -12.5 = -23.956439237 x = -23.956439237 Simplifying x = -23.956439237Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.043560763, -23.956439237}
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