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Simplifying x(25 + -1x) = 27.30 (25 * x + -1x * x) = 27.30 (25x + -1x2) = 27.30 Solving 25x + -1x2 = 27.30 Solving for variable 'x'. Reorder the terms: -27.30 + 25x + -1x2 = 27.30 + -27.30 Combine like terms: 27.30 + -27.30 = 0.00 -27.30 + 25x + -1x2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 27.3 + -25x + x2 = 0.00 Move the constant term to the right: Add '-27.3' to each side of the equation. 27.3 + -25x + -27.3 + x2 = 0.00 + -27.3 Reorder the terms: 27.3 + -27.3 + -25x + x2 = 0.00 + -27.3 Combine like terms: 27.3 + -27.3 = 0.0 0.0 + -25x + x2 = 0.00 + -27.3 -25x + x2 = 0.00 + -27.3 Combine like terms: 0.00 + -27.3 = -27.3 -25x + x2 = -27.3 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 = -27.3 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -27.3 + 156.25 Combine like terms: -27.3 + 156.25 = 128.95 156.25 + -25x + x2 = 128.95 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 128.95 Calculate the square root of the right side: 11.355615351 Break this problem into two subproblems by setting (x + -12.5) equal to 11.355615351 and -11.355615351.Subproblem 1
x + -12.5 = 11.355615351 Simplifying x + -12.5 = 11.355615351 Reorder the terms: -12.5 + x = 11.355615351 Solving -12.5 + x = 11.355615351 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 = 11.355615351 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 11.355615351 + 12.5 x = 11.355615351 + 12.5 Combine like terms: 11.355615351 + 12.5 = 23.855615351 x = 23.855615351 Simplifying x = 23.855615351Subproblem 2
x + -12.5 = -11.355615351 Simplifying x + -12.5 = -11.355615351 Reorder the terms: -12.5 + x = -11.355615351 Solving -12.5 + x = -11.355615351 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 = -11.355615351 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -11.355615351 + 12.5 x = -11.355615351 + 12.5 Combine like terms: -11.355615351 + 12.5 = 1.144384649 x = 1.144384649 Simplifying x = 1.144384649Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.855615351, 1.144384649}
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