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Simplifying x + -1(x + 17) = x(11 + -3x) Reorder the terms: x + -1(17 + x) = x(11 + -3x) x + (17 * -1 + x * -1) = x(11 + -3x) x + (-17 + -1x) = x(11 + -3x) Reorder the terms: -17 + x + -1x = x(11 + -3x) Combine like terms: x + -1x = 0 -17 + 0 = x(11 + -3x) -17 = x(11 + -3x) -17 = (11 * x + -3x * x) -17 = (11x + -3x2) Solving -17 = 11x + -3x2 Solving for variable 'x'. Reorder the terms: -17 + -11x + 3x2 = 11x + -11x + -3x2 + 3x2 Combine like terms: 11x + -11x = 0 -17 + -11x + 3x2 = 0 + -3x2 + 3x2 -17 + -11x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -17 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.666666667 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '5.666666667' to each side of the equation. -5.666666667 + -3.666666667x + 5.666666667 + x2 = 0 + 5.666666667 Reorder the terms: -5.666666667 + 5.666666667 + -3.666666667x + x2 = 0 + 5.666666667 Combine like terms: -5.666666667 + 5.666666667 = 0.000000000 0.000000000 + -3.666666667x + x2 = 0 + 5.666666667 -3.666666667x + x2 = 0 + 5.666666667 Combine like terms: 0 + 5.666666667 = 5.666666667 -3.666666667x + x2 = 5.666666667 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = 5.666666667 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 5.666666667 + 3.361111114 Combine like terms: 5.666666667 + 3.361111114 = 9.027777781 3.361111114 + -3.666666667x + x2 = 9.027777781 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 9.027777781 Calculate the square root of the right side: 3.004626063 Break this problem into two subproblems by setting (x + -1.833333334) equal to 3.004626063 and -3.004626063.Subproblem 1
x + -1.833333334 = 3.004626063 Simplifying x + -1.833333334 = 3.004626063 Reorder the terms: -1.833333334 + x = 3.004626063 Solving -1.833333334 + x = 3.004626063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 3.004626063 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 3.004626063 + 1.833333334 x = 3.004626063 + 1.833333334 Combine like terms: 3.004626063 + 1.833333334 = 4.837959397 x = 4.837959397 Simplifying x = 4.837959397Subproblem 2
x + -1.833333334 = -3.004626063 Simplifying x + -1.833333334 = -3.004626063 Reorder the terms: -1.833333334 + x = -3.004626063 Solving -1.833333334 + x = -3.004626063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -3.004626063 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -3.004626063 + 1.833333334 x = -3.004626063 + 1.833333334 Combine like terms: -3.004626063 + 1.833333334 = -1.171292729 x = -1.171292729 Simplifying x = -1.171292729Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.837959397, -1.171292729}
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