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Simplifying 5(x + -3)(x + 8) + 9(x + -3) = 2 Reorder the terms: 5(-3 + x)(x + 8) + 9(x + -3) = 2 Reorder the terms: 5(-3 + x)(8 + x) + 9(x + -3) = 2 Multiply (-3 + x) * (8 + x) 5(-3(8 + x) + x(8 + x)) + 9(x + -3) = 2 5((8 * -3 + x * -3) + x(8 + x)) + 9(x + -3) = 2 5((-24 + -3x) + x(8 + x)) + 9(x + -3) = 2 5(-24 + -3x + (8 * x + x * x)) + 9(x + -3) = 2 5(-24 + -3x + (8x + x2)) + 9(x + -3) = 2 Combine like terms: -3x + 8x = 5x 5(-24 + 5x + x2) + 9(x + -3) = 2 (-24 * 5 + 5x * 5 + x2 * 5) + 9(x + -3) = 2 (-120 + 25x + 5x2) + 9(x + -3) = 2 Reorder the terms: -120 + 25x + 5x2 + 9(-3 + x) = 2 -120 + 25x + 5x2 + (-3 * 9 + x * 9) = 2 -120 + 25x + 5x2 + (-27 + 9x) = 2 Reorder the terms: -120 + -27 + 25x + 9x + 5x2 = 2 Combine like terms: -120 + -27 = -147 -147 + 25x + 9x + 5x2 = 2 Combine like terms: 25x + 9x = 34x -147 + 34x + 5x2 = 2 Solving -147 + 34x + 5x2 = 2 Solving for variable 'x'. Reorder the terms: -147 + -2 + 34x + 5x2 = 2 + -2 Combine like terms: -147 + -2 = -149 -149 + 34x + 5x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -149 + 34x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -29.8 + 6.8x + x2 = 0 Move the constant term to the right: Add '29.8' to each side of the equation. -29.8 + 6.8x + 29.8 + x2 = 0 + 29.8 Reorder the terms: -29.8 + 29.8 + 6.8x + x2 = 0 + 29.8 Combine like terms: -29.8 + 29.8 = 0.0 0.0 + 6.8x + x2 = 0 + 29.8 6.8x + x2 = 0 + 29.8 Combine like terms: 0 + 29.8 = 29.8 6.8x + x2 = 29.8 The x term is 6.8x. Take half its coefficient (3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. 6.8x + 11.56 + x2 = 29.8 + 11.56 Reorder the terms: 11.56 + 6.8x + x2 = 29.8 + 11.56 Combine like terms: 29.8 + 11.56 = 41.36 11.56 + 6.8x + x2 = 41.36 Factor a perfect square on the left side: (x + 3.4)(x + 3.4) = 41.36 Calculate the square root of the right side: 6.431174076 Break this problem into two subproblems by setting (x + 3.4) equal to 6.431174076 and -6.431174076.Subproblem 1
x + 3.4 = 6.431174076 Simplifying x + 3.4 = 6.431174076 Reorder the terms: 3.4 + x = 6.431174076 Solving 3.4 + x = 6.431174076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + x = 6.431174076 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = 6.431174076 + -3.4 x = 6.431174076 + -3.4 Combine like terms: 6.431174076 + -3.4 = 3.031174076 x = 3.031174076 Simplifying x = 3.031174076Subproblem 2
x + 3.4 = -6.431174076 Simplifying x + 3.4 = -6.431174076 Reorder the terms: 3.4 + x = -6.431174076 Solving 3.4 + x = -6.431174076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + x = -6.431174076 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = -6.431174076 + -3.4 x = -6.431174076 + -3.4 Combine like terms: -6.431174076 + -3.4 = -9.831174076 x = -9.831174076 Simplifying x = -9.831174076Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.031174076, -9.831174076}
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