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Simplifying (9x + -25) + -1(4x + -2)(2x + -9) + -1(x + -3)(x + 3) = 0 Reorder the terms: (-25 + 9x) + -1(4x + -2)(2x + -9) + -1(x + -3)(x + 3) = 0 Remove parenthesis around (-25 + 9x) -25 + 9x + -1(4x + -2)(2x + -9) + -1(x + -3)(x + 3) = 0 Reorder the terms: -25 + 9x + -1(-2 + 4x)(2x + -9) + -1(x + -3)(x + 3) = 0 Reorder the terms: -25 + 9x + -1(-2 + 4x)(-9 + 2x) + -1(x + -3)(x + 3) = 0 Multiply (-2 + 4x) * (-9 + 2x) -25 + 9x + -1(-2(-9 + 2x) + 4x * (-9 + 2x)) + -1(x + -3)(x + 3) = 0 -25 + 9x + -1((-9 * -2 + 2x * -2) + 4x * (-9 + 2x)) + -1(x + -3)(x + 3) = 0 -25 + 9x + -1((18 + -4x) + 4x * (-9 + 2x)) + -1(x + -3)(x + 3) = 0 -25 + 9x + -1(18 + -4x + (-9 * 4x + 2x * 4x)) + -1(x + -3)(x + 3) = 0 -25 + 9x + -1(18 + -4x + (-36x + 8x2)) + -1(x + -3)(x + 3) = 0 Combine like terms: -4x + -36x = -40x -25 + 9x + -1(18 + -40x + 8x2) + -1(x + -3)(x + 3) = 0 -25 + 9x + (18 * -1 + -40x * -1 + 8x2 * -1) + -1(x + -3)(x + 3) = 0 -25 + 9x + (-18 + 40x + -8x2) + -1(x + -3)(x + 3) = 0 Reorder the terms: -25 + 9x + -18 + 40x + -8x2 + -1(-3 + x)(x + 3) = 0 Reorder the terms: -25 + 9x + -18 + 40x + -8x2 + -1(-3 + x)(3 + x) = 0 Multiply (-3 + x) * (3 + x) -25 + 9x + -18 + 40x + -8x2 + -1(-3(3 + x) + x(3 + x)) = 0 -25 + 9x + -18 + 40x + -8x2 + -1((3 * -3 + x * -3) + x(3 + x)) = 0 -25 + 9x + -18 + 40x + -8x2 + -1((-9 + -3x) + x(3 + x)) = 0 -25 + 9x + -18 + 40x + -8x2 + -1(-9 + -3x + (3 * x + x * x)) = 0 -25 + 9x + -18 + 40x + -8x2 + -1(-9 + -3x + (3x + x2)) = 0 Combine like terms: -3x + 3x = 0 -25 + 9x + -18 + 40x + -8x2 + -1(-9 + 0 + x2) = 0 -25 + 9x + -18 + 40x + -8x2 + -1(-9 + x2) = 0 -25 + 9x + -18 + 40x + -8x2 + (-9 * -1 + x2 * -1) = 0 -25 + 9x + -18 + 40x + -8x2 + (9 + -1x2) = 0 Reorder the terms: -25 + -18 + 9 + 9x + 40x + -8x2 + -1x2 = 0 Combine like terms: -25 + -18 = -43 -43 + 9 + 9x + 40x + -8x2 + -1x2 = 0 Combine like terms: -43 + 9 = -34 -34 + 9x + 40x + -8x2 + -1x2 = 0 Combine like terms: 9x + 40x = 49x -34 + 49x + -8x2 + -1x2 = 0 Combine like terms: -8x2 + -1x2 = -9x2 -34 + 49x + -9x2 = 0 Solving -34 + 49x + -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'. 3.777777778 + -5.444444444x + x2 = 0 Move the constant term to the right: Add '-3.777777778' to each side of the equation. 3.777777778 + -5.444444444x + -3.777777778 + x2 = 0 + -3.777777778 Reorder the terms: 3.777777778 + -3.777777778 + -5.444444444x + x2 = 0 + -3.777777778 Combine like terms: 3.777777778 + -3.777777778 = 0.000000000 0.000000000 + -5.444444444x + x2 = 0 + -3.777777778 -5.444444444x + x2 = 0 + -3.777777778 Combine like terms: 0 + -3.777777778 = -3.777777778 -5.444444444x + x2 = -3.777777778 The x term is -5.444444444x. Take half its coefficient (-2.722222222). Square it (7.410493826) and add it to both sides. Add '7.410493826' to each side of the equation. -5.444444444x + 7.410493826 + x2 = -3.777777778 + 7.410493826 Reorder the terms: 7.410493826 + -5.444444444x + x2 = -3.777777778 + 7.410493826 Combine like terms: -3.777777778 + 7.410493826 = 3.632716048 7.410493826 + -5.444444444x + x2 = 3.632716048 Factor a perfect square on the left side: (x + -2.722222222)(x + -2.722222222) = 3.632716048 Calculate the square root of the right side: 1.905968533 Break this problem into two subproblems by setting (x + -2.722222222) equal to 1.905968533 and -1.905968533.Subproblem 1
x + -2.722222222 = 1.905968533 Simplifying x + -2.722222222 = 1.905968533 Reorder the terms: -2.722222222 + x = 1.905968533 Solving -2.722222222 + x = 1.905968533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.722222222' to each side of the equation. -2.722222222 + 2.722222222 + x = 1.905968533 + 2.722222222 Combine like terms: -2.722222222 + 2.722222222 = 0.000000000 0.000000000 + x = 1.905968533 + 2.722222222 x = 1.905968533 + 2.722222222 Combine like terms: 1.905968533 + 2.722222222 = 4.628190755 x = 4.628190755 Simplifying x = 4.628190755Subproblem 2
x + -2.722222222 = -1.905968533 Simplifying x + -2.722222222 = -1.905968533 Reorder the terms: -2.722222222 + x = -1.905968533 Solving -2.722222222 + x = -1.905968533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.722222222' to each side of the equation. -2.722222222 + 2.722222222 + x = -1.905968533 + 2.722222222 Combine like terms: -2.722222222 + 2.722222222 = 0.000000000 0.000000000 + x = -1.905968533 + 2.722222222 x = -1.905968533 + 2.722222222 Combine like terms: -1.905968533 + 2.722222222 = 0.816253689 x = 0.816253689 Simplifying x = 0.816253689Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.628190755, 0.816253689}
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