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Simplifying 100x2 + -2500x + 156.25 = 0 Reorder the terms: 156.25 + -2500x + 100x2 = 0 Solving 156.25 + -2500x + 100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. 1.5625 + -25x + x2 = 0 Move the constant term to the right: Add '-1.5625' to each side of the equation. 1.5625 + -25x + -1.5625 + x2 = 0 + -1.5625 Reorder the terms: 1.5625 + -1.5625 + -25x + x2 = 0 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + -25x + x2 = 0 + -1.5625 -25x + x2 = 0 + -1.5625 Combine like terms: 0 + -1.5625 = -1.5625 -25x + x2 = -1.5625 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 = -1.5625 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -1.5625 + 156.25 Combine like terms: -1.5625 + 156.25 = 154.6875 156.25 + -25x + x2 = 154.6875 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 154.6875 Calculate the square root of the right side: 12.437342964 Break this problem into two subproblems by setting (x + -12.5) equal to 12.437342964 and -12.437342964.Subproblem 1
x + -12.5 = 12.437342964 Simplifying x + -12.5 = 12.437342964 Reorder the terms: -12.5 + x = 12.437342964 Solving -12.5 + x = 12.437342964 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 = 12.437342964 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 12.437342964 + 12.5 x = 12.437342964 + 12.5 Combine like terms: 12.437342964 + 12.5 = 24.937342964 x = 24.937342964 Simplifying x = 24.937342964Subproblem 2
x + -12.5 = -12.437342964 Simplifying x + -12.5 = -12.437342964 Reorder the terms: -12.5 + x = -12.437342964 Solving -12.5 + x = -12.437342964 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 = -12.437342964 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -12.437342964 + 12.5 x = -12.437342964 + 12.5 Combine like terms: -12.437342964 + 12.5 = 0.062657036 x = 0.062657036 Simplifying x = 0.062657036Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.937342964, 0.062657036}
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