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Simplifying (6x + -10) + -1(4x + -2)(2x + -9) + -1(x + -3)(x + 3) = 0 Reorder the terms: (-10 + 6x) + -1(4x + -2)(2x + -9) + -1(x + -3)(x + 3) = 0 Remove parenthesis around (-10 + 6x) -10 + 6x + -1(4x + -2)(2x + -9) + -1(x + -3)(x + 3) = 0 Reorder the terms: -10 + 6x + -1(-2 + 4x)(2x + -9) + -1(x + -3)(x + 3) = 0 Reorder the terms: -10 + 6x + -1(-2 + 4x)(-9 + 2x) + -1(x + -3)(x + 3) = 0 Multiply (-2 + 4x) * (-9 + 2x) -10 + 6x + -1(-2(-9 + 2x) + 4x * (-9 + 2x)) + -1(x + -3)(x + 3) = 0 -10 + 6x + -1((-9 * -2 + 2x * -2) + 4x * (-9 + 2x)) + -1(x + -3)(x + 3) = 0 -10 + 6x + -1((18 + -4x) + 4x * (-9 + 2x)) + -1(x + -3)(x + 3) = 0 -10 + 6x + -1(18 + -4x + (-9 * 4x + 2x * 4x)) + -1(x + -3)(x + 3) = 0 -10 + 6x + -1(18 + -4x + (-36x + 8x2)) + -1(x + -3)(x + 3) = 0 Combine like terms: -4x + -36x = -40x -10 + 6x + -1(18 + -40x + 8x2) + -1(x + -3)(x + 3) = 0 -10 + 6x + (18 * -1 + -40x * -1 + 8x2 * -1) + -1(x + -3)(x + 3) = 0 -10 + 6x + (-18 + 40x + -8x2) + -1(x + -3)(x + 3) = 0 Reorder the terms: -10 + 6x + -18 + 40x + -8x2 + -1(-3 + x)(x + 3) = 0 Reorder the terms: -10 + 6x + -18 + 40x + -8x2 + -1(-3 + x)(3 + x) = 0 Multiply (-3 + x) * (3 + x) -10 + 6x + -18 + 40x + -8x2 + -1(-3(3 + x) + x(3 + x)) = 0 -10 + 6x + -18 + 40x + -8x2 + -1((3 * -3 + x * -3) + x(3 + x)) = 0 -10 + 6x + -18 + 40x + -8x2 + -1((-9 + -3x) + x(3 + x)) = 0 -10 + 6x + -18 + 40x + -8x2 + -1(-9 + -3x + (3 * x + x * x)) = 0 -10 + 6x + -18 + 40x + -8x2 + -1(-9 + -3x + (3x + x2)) = 0 Combine like terms: -3x + 3x = 0 -10 + 6x + -18 + 40x + -8x2 + -1(-9 + 0 + x2) = 0 -10 + 6x + -18 + 40x + -8x2 + -1(-9 + x2) = 0 -10 + 6x + -18 + 40x + -8x2 + (-9 * -1 + x2 * -1) = 0 -10 + 6x + -18 + 40x + -8x2 + (9 + -1x2) = 0 Reorder the terms: -10 + -18 + 9 + 6x + 40x + -8x2 + -1x2 = 0 Combine like terms: -10 + -18 = -28 -28 + 9 + 6x + 40x + -8x2 + -1x2 = 0 Combine like terms: -28 + 9 = -19 -19 + 6x + 40x + -8x2 + -1x2 = 0 Combine like terms: 6x + 40x = 46x -19 + 46x + -8x2 + -1x2 = 0 Combine like terms: -8x2 + -1x2 = -9x2 -19 + 46x + -9x2 = 0 Solving -19 + 46x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 2.111111111 + -5.111111111x + x2 = 0 Move the constant term to the right: Add '-2.111111111' to each side of the equation. 2.111111111 + -5.111111111x + -2.111111111 + x2 = 0 + -2.111111111 Reorder the terms: 2.111111111 + -2.111111111 + -5.111111111x + x2 = 0 + -2.111111111 Combine like terms: 2.111111111 + -2.111111111 = 0.000000000 0.000000000 + -5.111111111x + x2 = 0 + -2.111111111 -5.111111111x + x2 = 0 + -2.111111111 Combine like terms: 0 + -2.111111111 = -2.111111111 -5.111111111x + x2 = -2.111111111 The x term is -5.111111111x. Take half its coefficient (-2.555555556). Square it (6.530864200) and add it to both sides. Add '6.530864200' to each side of the equation. -5.111111111x + 6.530864200 + x2 = -2.111111111 + 6.530864200 Reorder the terms: 6.530864200 + -5.111111111x + x2 = -2.111111111 + 6.530864200 Combine like terms: -2.111111111 + 6.530864200 = 4.419753089 6.530864200 + -5.111111111x + x2 = 4.419753089 Factor a perfect square on the left side: (x + -2.555555556)(x + -2.555555556) = 4.419753089 Calculate the square root of the right side: 2.102320882 Break this problem into two subproblems by setting (x + -2.555555556) equal to 2.102320882 and -2.102320882.Subproblem 1
x + -2.555555556 = 2.102320882 Simplifying x + -2.555555556 = 2.102320882 Reorder the terms: -2.555555556 + x = 2.102320882 Solving -2.555555556 + x = 2.102320882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.555555556' to each side of the equation. -2.555555556 + 2.555555556 + x = 2.102320882 + 2.555555556 Combine like terms: -2.555555556 + 2.555555556 = 0.000000000 0.000000000 + x = 2.102320882 + 2.555555556 x = 2.102320882 + 2.555555556 Combine like terms: 2.102320882 + 2.555555556 = 4.657876438 x = 4.657876438 Simplifying x = 4.657876438Subproblem 2
x + -2.555555556 = -2.102320882 Simplifying x + -2.555555556 = -2.102320882 Reorder the terms: -2.555555556 + x = -2.102320882 Solving -2.555555556 + x = -2.102320882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.555555556' to each side of the equation. -2.555555556 + 2.555555556 + x = -2.102320882 + 2.555555556 Combine like terms: -2.555555556 + 2.555555556 = 0.000000000 0.000000000 + x = -2.102320882 + 2.555555556 x = -2.102320882 + 2.555555556 Combine like terms: -2.102320882 + 2.555555556 = 0.453234674 x = 0.453234674 Simplifying x = 0.453234674Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.657876438, 0.453234674}
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