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Simplifying 2x[11(x + -4) + 3] = 77 Reorder the terms: 2x[11(-4 + x) + 3] = 77 2x[(-4 * 11 + x * 11) + 3] = 77 2x[(-44 + 11x) + 3] = 77 Reorder the terms: 2x[-44 + 3 + 11x] = 77 Combine like terms: -44 + 3 = -41 2x[-41 + 11x] = 77 [-41 * 2x + 11x * 2x] = 77 [-82x + 22x2] = 77 Solving -82x + 22x2 = 77 Solving for variable 'x'. Reorder the terms: -77 + -82x + 22x2 = 77 + -77 Combine like terms: 77 + -77 = 0 -77 + -82x + 22x2 = 0 Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -3.5 + -3.727272727x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -3.727272727x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -3.727272727x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -3.727272727x + x2 = 0 + 3.5 -3.727272727x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -3.727272727x + x2 = 3.5 The x term is -3.727272727x. Take half its coefficient (-1.863636364). Square it (3.473140497) and add it to both sides. Add '3.473140497' to each side of the equation. -3.727272727x + 3.473140497 + x2 = 3.5 + 3.473140497 Reorder the terms: 3.473140497 + -3.727272727x + x2 = 3.5 + 3.473140497 Combine like terms: 3.5 + 3.473140497 = 6.973140497 3.473140497 + -3.727272727x + x2 = 6.973140497 Factor a perfect square on the left side: (x + -1.863636364)(x + -1.863636364) = 6.973140497 Calculate the square root of the right side: 2.640670464 Break this problem into two subproblems by setting (x + -1.863636364) equal to 2.640670464 and -2.640670464.Subproblem 1
x + -1.863636364 = 2.640670464 Simplifying x + -1.863636364 = 2.640670464 Reorder the terms: -1.863636364 + x = 2.640670464 Solving -1.863636364 + x = 2.640670464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.863636364' to each side of the equation. -1.863636364 + 1.863636364 + x = 2.640670464 + 1.863636364 Combine like terms: -1.863636364 + 1.863636364 = 0.000000000 0.000000000 + x = 2.640670464 + 1.863636364 x = 2.640670464 + 1.863636364 Combine like terms: 2.640670464 + 1.863636364 = 4.504306828 x = 4.504306828 Simplifying x = 4.504306828Subproblem 2
x + -1.863636364 = -2.640670464 Simplifying x + -1.863636364 = -2.640670464 Reorder the terms: -1.863636364 + x = -2.640670464 Solving -1.863636364 + x = -2.640670464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.863636364' to each side of the equation. -1.863636364 + 1.863636364 + x = -2.640670464 + 1.863636364 Combine like terms: -1.863636364 + 1.863636364 = 0.000000000 0.000000000 + x = -2.640670464 + 1.863636364 x = -2.640670464 + 1.863636364 Combine like terms: -2.640670464 + 1.863636364 = -0.7770341 x = -0.7770341 Simplifying x = -0.7770341Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.504306828, -0.7770341}
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