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Simplifying 5x2 + -125x + 312.5 = 0 Reorder the terms: 312.5 + -125x + 5x2 = 0 Solving 312.5 + -125x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 62.5 + -25x + x2 = 0 Move the constant term to the right: Add '-62.5' to each side of the equation. 62.5 + -25x + -62.5 + x2 = 0 + -62.5 Reorder the terms: 62.5 + -62.5 + -25x + x2 = 0 + -62.5 Combine like terms: 62.5 + -62.5 = 0.0 0.0 + -25x + x2 = 0 + -62.5 -25x + x2 = 0 + -62.5 Combine like terms: 0 + -62.5 = -62.5 -25x + x2 = -62.5 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 = -62.5 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -62.5 + 156.25 Combine like terms: -62.5 + 156.25 = 93.75 156.25 + -25x + x2 = 93.75 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 93.75 Calculate the square root of the right side: 9.682458366 Break this problem into two subproblems by setting (x + -12.5) equal to 9.682458366 and -9.682458366.Subproblem 1
x + -12.5 = 9.682458366 Simplifying x + -12.5 = 9.682458366 Reorder the terms: -12.5 + x = 9.682458366 Solving -12.5 + x = 9.682458366 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 = 9.682458366 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 9.682458366 + 12.5 x = 9.682458366 + 12.5 Combine like terms: 9.682458366 + 12.5 = 22.182458366 x = 22.182458366 Simplifying x = 22.182458366Subproblem 2
x + -12.5 = -9.682458366 Simplifying x + -12.5 = -9.682458366 Reorder the terms: -12.5 + x = -9.682458366 Solving -12.5 + x = -9.682458366 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 = -9.682458366 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -9.682458366 + 12.5 x = -9.682458366 + 12.5 Combine like terms: -9.682458366 + 12.5 = 2.817541634 x = 2.817541634 Simplifying x = 2.817541634Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.182458366, 2.817541634}
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