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Simplifying x2 + 25x = 5 Reorder the terms: 25x + x2 = 5 Solving 25x + x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 25x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 25x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 25x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 25x + x2 = 0 + 5 25x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 25x + x2 = 5 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 = 5 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 5 + 156.25 Combine like terms: 5 + 156.25 = 161.25 156.25 + 25x + x2 = 161.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 161.25 Calculate the square root of the right side: 12.698425099 Break this problem into two subproblems by setting (x + 12.5) equal to 12.698425099 and -12.698425099.Subproblem 1
x + 12.5 = 12.698425099 Simplifying x + 12.5 = 12.698425099 Reorder the terms: 12.5 + x = 12.698425099 Solving 12.5 + x = 12.698425099 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 = 12.698425099 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 12.698425099 + -12.5 x = 12.698425099 + -12.5 Combine like terms: 12.698425099 + -12.5 = 0.198425099 x = 0.198425099 Simplifying x = 0.198425099Subproblem 2
x + 12.5 = -12.698425099 Simplifying x + 12.5 = -12.698425099 Reorder the terms: 12.5 + x = -12.698425099 Solving 12.5 + x = -12.698425099 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 = -12.698425099 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -12.698425099 + -12.5 x = -12.698425099 + -12.5 Combine like terms: -12.698425099 + -12.5 = -25.198425099 x = -25.198425099 Simplifying x = -25.198425099Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.198425099, -25.198425099}
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