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Simplifying 25x + x2 = 169 Solving 25x + x2 = 169 Solving for variable 'x'. Reorder the terms: -169 + 25x + x2 = 169 + -169 Combine like terms: 169 + -169 = 0 -169 + 25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '169' to each side of the equation. -169 + 25x + 169 + x2 = 0 + 169 Reorder the terms: -169 + 169 + 25x + x2 = 0 + 169 Combine like terms: -169 + 169 = 0 0 + 25x + x2 = 0 + 169 25x + x2 = 0 + 169 Combine like terms: 0 + 169 = 169 25x + x2 = 169 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 = 169 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 169 + 156.25 Combine like terms: 169 + 156.25 = 325.25 156.25 + 25x + x2 = 325.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 325.25 Calculate the square root of the right side: 18.034688797 Break this problem into two subproblems by setting (x + 12.5) equal to 18.034688797 and -18.034688797.Subproblem 1
x + 12.5 = 18.034688797 Simplifying x + 12.5 = 18.034688797 Reorder the terms: 12.5 + x = 18.034688797 Solving 12.5 + x = 18.034688797 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 = 18.034688797 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 18.034688797 + -12.5 x = 18.034688797 + -12.5 Combine like terms: 18.034688797 + -12.5 = 5.534688797 x = 5.534688797 Simplifying x = 5.534688797Subproblem 2
x + 12.5 = -18.034688797 Simplifying x + 12.5 = -18.034688797 Reorder the terms: 12.5 + x = -18.034688797 Solving 12.5 + x = -18.034688797 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 = -18.034688797 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -18.034688797 + -12.5 x = -18.034688797 + -12.5 Combine like terms: -18.034688797 + -12.5 = -30.534688797 x = -30.534688797 Simplifying x = -30.534688797Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.534688797, -30.534688797}
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