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Simplifying 7x + -10 = 6x(11 + -2x) Reorder the terms: -10 + 7x = 6x(11 + -2x) -10 + 7x = (11 * 6x + -2x * 6x) -10 + 7x = (66x + -12x2) Solving -10 + 7x = 66x + -12x2 Solving for variable 'x'. Combine like terms: 7x + -66x = -59x -10 + -59x + 12x2 = 66x + -12x2 + -66x + 12x2 Reorder the terms: -10 + -59x + 12x2 = 66x + -66x + -12x2 + 12x2 Combine like terms: 66x + -66x = 0 -10 + -59x + 12x2 = 0 + -12x2 + 12x2 -10 + -59x + 12x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 -10 + -59x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.8333333333 + -4.916666667x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -4.916666667x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -4.916666667x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -4.916666667x + x2 = 0 + 0.8333333333 -4.916666667x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -4.916666667x + x2 = 0.8333333333 The x term is -4.916666667x. Take half its coefficient (-2.458333334). Square it (6.043402781) and add it to both sides. Add '6.043402781' to each side of the equation. -4.916666667x + 6.043402781 + x2 = 0.8333333333 + 6.043402781 Reorder the terms: 6.043402781 + -4.916666667x + x2 = 0.8333333333 + 6.043402781 Combine like terms: 0.8333333333 + 6.043402781 = 6.8767361143 6.043402781 + -4.916666667x + x2 = 6.8767361143 Factor a perfect square on the left side: (x + -2.458333334)(x + -2.458333334) = 6.8767361143 Calculate the square root of the right side: 2.622353164 Break this problem into two subproblems by setting (x + -2.458333334) equal to 2.622353164 and -2.622353164.Subproblem 1
x + -2.458333334 = 2.622353164 Simplifying x + -2.458333334 = 2.622353164 Reorder the terms: -2.458333334 + x = 2.622353164 Solving -2.458333334 + x = 2.622353164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.458333334' to each side of the equation. -2.458333334 + 2.458333334 + x = 2.622353164 + 2.458333334 Combine like terms: -2.458333334 + 2.458333334 = 0.000000000 0.000000000 + x = 2.622353164 + 2.458333334 x = 2.622353164 + 2.458333334 Combine like terms: 2.622353164 + 2.458333334 = 5.080686498 x = 5.080686498 Simplifying x = 5.080686498Subproblem 2
x + -2.458333334 = -2.622353164 Simplifying x + -2.458333334 = -2.622353164 Reorder the terms: -2.458333334 + x = -2.622353164 Solving -2.458333334 + x = -2.622353164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.458333334' to each side of the equation. -2.458333334 + 2.458333334 + x = -2.622353164 + 2.458333334 Combine like terms: -2.458333334 + 2.458333334 = 0.000000000 0.000000000 + x = -2.622353164 + 2.458333334 x = -2.622353164 + 2.458333334 Combine like terms: -2.622353164 + 2.458333334 = -0.16401983 x = -0.16401983 Simplifying x = -0.16401983Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.080686498, -0.16401983}
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