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Simplifying 11x(19 + -1x) = 196 (19 * 11x + -1x * 11x) = 196 (209x + -11x2) = 196 Solving 209x + -11x2 = 196 Solving for variable 'x'. Reorder the terms: -196 + 209x + -11x2 = 196 + -196 Combine like terms: 196 + -196 = 0 -196 + 209x + -11x2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. 17.81818182 + -19x + x2 = 0 Move the constant term to the right: Add '-17.81818182' to each side of the equation. 17.81818182 + -19x + -17.81818182 + x2 = 0 + -17.81818182 Reorder the terms: 17.81818182 + -17.81818182 + -19x + x2 = 0 + -17.81818182 Combine like terms: 17.81818182 + -17.81818182 = 0.00000000 0.00000000 + -19x + x2 = 0 + -17.81818182 -19x + x2 = 0 + -17.81818182 Combine like terms: 0 + -17.81818182 = -17.81818182 -19x + x2 = -17.81818182 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 = -17.81818182 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -17.81818182 + 90.25 Combine like terms: -17.81818182 + 90.25 = 72.43181818 90.25 + -19x + x2 = 72.43181818 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 72.43181818 Calculate the square root of the right side: 8.510688467 Break this problem into two subproblems by setting (x + -9.5) equal to 8.510688467 and -8.510688467.Subproblem 1
x + -9.5 = 8.510688467 Simplifying x + -9.5 = 8.510688467 Reorder the terms: -9.5 + x = 8.510688467 Solving -9.5 + x = 8.510688467 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 = 8.510688467 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 8.510688467 + 9.5 x = 8.510688467 + 9.5 Combine like terms: 8.510688467 + 9.5 = 18.010688467 x = 18.010688467 Simplifying x = 18.010688467Subproblem 2
x + -9.5 = -8.510688467 Simplifying x + -9.5 = -8.510688467 Reorder the terms: -9.5 + x = -8.510688467 Solving -9.5 + x = -8.510688467 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 = -8.510688467 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -8.510688467 + 9.5 x = -8.510688467 + 9.5 Combine like terms: -8.510688467 + 9.5 = 0.989311533 x = 0.989311533 Simplifying x = 0.989311533Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.010688467, 0.989311533}
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