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Simplifying 101.25 = -25x + 5x2 Solving 101.25 = -25x + 5x2 Solving for variable 'x'. Reorder the terms: 101.25 + 25x + -5x2 = -25x + 25x + 5x2 + -5x2 Combine like terms: -25x + 25x = 0 101.25 + 25x + -5x2 = 0 + 5x2 + -5x2 101.25 + 25x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 101.25 + 25x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -20.25 + -5x + x2 = 0 Move the constant term to the right: Add '20.25' to each side of the equation. -20.25 + -5x + 20.25 + x2 = 0 + 20.25 Reorder the terms: -20.25 + 20.25 + -5x + x2 = 0 + 20.25 Combine like terms: -20.25 + 20.25 = 0.00 0.00 + -5x + x2 = 0 + 20.25 -5x + x2 = 0 + 20.25 Combine like terms: 0 + 20.25 = 20.25 -5x + x2 = 20.25 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 20.25 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 20.25 + 6.25 Combine like terms: 20.25 + 6.25 = 26.5 6.25 + -5x + x2 = 26.5 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 26.5 Calculate the square root of the right side: 5.14781507 Break this problem into two subproblems by setting (x + -2.5) equal to 5.14781507 and -5.14781507.Subproblem 1
x + -2.5 = 5.14781507 Simplifying x + -2.5 = 5.14781507 Reorder the terms: -2.5 + x = 5.14781507 Solving -2.5 + x = 5.14781507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 5.14781507 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.14781507 + 2.5 x = 5.14781507 + 2.5 Combine like terms: 5.14781507 + 2.5 = 7.64781507 x = 7.64781507 Simplifying x = 7.64781507Subproblem 2
x + -2.5 = -5.14781507 Simplifying x + -2.5 = -5.14781507 Reorder the terms: -2.5 + x = -5.14781507 Solving -2.5 + x = -5.14781507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -5.14781507 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.14781507 + 2.5 x = -5.14781507 + 2.5 Combine like terms: -5.14781507 + 2.5 = -2.64781507 x = -2.64781507 Simplifying x = -2.64781507Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.64781507, -2.64781507}
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