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Simplifying x * 25 + x2 = 135 Reorder the terms for easier multiplication: 25x + x2 = 135 Solving 25x + x2 = 135 Solving for variable 'x'. Reorder the terms: -135 + 25x + x2 = 135 + -135 Combine like terms: 135 + -135 = 0 -135 + 25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '135' to each side of the equation. -135 + 25x + 135 + x2 = 0 + 135 Reorder the terms: -135 + 135 + 25x + x2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + 25x + x2 = 0 + 135 25x + x2 = 0 + 135 Combine like terms: 0 + 135 = 135 25x + x2 = 135 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 = 135 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 135 + 156.25 Combine like terms: 135 + 156.25 = 291.25 156.25 + 25x + x2 = 291.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 291.25 Calculate the square root of the right side: 17.066048166 Break this problem into two subproblems by setting (x + 12.5) equal to 17.066048166 and -17.066048166.Subproblem 1
x + 12.5 = 17.066048166 Simplifying x + 12.5 = 17.066048166 Reorder the terms: 12.5 + x = 17.066048166 Solving 12.5 + x = 17.066048166 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 = 17.066048166 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 17.066048166 + -12.5 x = 17.066048166 + -12.5 Combine like terms: 17.066048166 + -12.5 = 4.566048166 x = 4.566048166 Simplifying x = 4.566048166Subproblem 2
x + 12.5 = -17.066048166 Simplifying x + 12.5 = -17.066048166 Reorder the terms: 12.5 + x = -17.066048166 Solving 12.5 + x = -17.066048166 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 = -17.066048166 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -17.066048166 + -12.5 x = -17.066048166 + -12.5 Combine like terms: -17.066048166 + -12.5 = -29.566048166 x = -29.566048166 Simplifying x = -29.566048166Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.566048166, -29.566048166}
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