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Simplifying 2x(-1x + 19) = 27 Reorder the terms: 2x(19 + -1x) = 27 (19 * 2x + -1x * 2x) = 27 (38x + -2x2) = 27 Solving 38x + -2x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + 38x + -2x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 38x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 13.5 + -19x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + -19x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + -19x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -19x + x2 = 0 + -13.5 -19x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 -19x + x2 = -13.5 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -13.5 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -13.5 + 90.25 Combine like terms: -13.5 + 90.25 = 76.75 90.25 + -19x + x2 = 76.75 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 76.75 Calculate the square root of the right side: 8.760707734 Break this problem into two subproblems by setting (x + -9.5) equal to 8.760707734 and -8.760707734.Subproblem 1
x + -9.5 = 8.760707734 Simplifying x + -9.5 = 8.760707734 Reorder the terms: -9.5 + x = 8.760707734 Solving -9.5 + x = 8.760707734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 8.760707734 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 8.760707734 + 9.5 x = 8.760707734 + 9.5 Combine like terms: 8.760707734 + 9.5 = 18.260707734 x = 18.260707734 Simplifying x = 18.260707734Subproblem 2
x + -9.5 = -8.760707734 Simplifying x + -9.5 = -8.760707734 Reorder the terms: -9.5 + x = -8.760707734 Solving -9.5 + x = -8.760707734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -8.760707734 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -8.760707734 + 9.5 x = -8.760707734 + 9.5 Combine like terms: -8.760707734 + 9.5 = 0.739292266 x = 0.739292266 Simplifying x = 0.739292266Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.260707734, 0.739292266}
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