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Simplifying (5x + 3)(x + -6) = 9 Reorder the terms: (3 + 5x)(x + -6) = 9 Reorder the terms: (3 + 5x)(-6 + x) = 9 Multiply (3 + 5x) * (-6 + x) (3(-6 + x) + 5x * (-6 + x)) = 9 ((-6 * 3 + x * 3) + 5x * (-6 + x)) = 9 ((-18 + 3x) + 5x * (-6 + x)) = 9 (-18 + 3x + (-6 * 5x + x * 5x)) = 9 (-18 + 3x + (-30x + 5x2)) = 9 Combine like terms: 3x + -30x = -27x (-18 + -27x + 5x2) = 9 Solving -18 + -27x + 5x2 = 9 Solving for variable 'x'. Reorder the terms: -18 + -9 + -27x + 5x2 = 9 + -9 Combine like terms: -18 + -9 = -27 -27 + -27x + 5x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -27 + -27x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.4 + -5.4x + x2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + -5.4x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + -5.4x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + -5.4x + x2 = 0 + 5.4 -5.4x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 -5.4x + x2 = 5.4 The x term is -5.4x. Take half its coefficient (-2.7). Square it (7.29) and add it to both sides. Add '7.29' to each side of the equation. -5.4x + 7.29 + x2 = 5.4 + 7.29 Reorder the terms: 7.29 + -5.4x + x2 = 5.4 + 7.29 Combine like terms: 5.4 + 7.29 = 12.69 7.29 + -5.4x + x2 = 12.69 Factor a perfect square on the left side: (x + -2.7)(x + -2.7) = 12.69 Calculate the square root of the right side: 3.562302626 Break this problem into two subproblems by setting (x + -2.7) equal to 3.562302626 and -3.562302626.Subproblem 1
x + -2.7 = 3.562302626 Simplifying x + -2.7 = 3.562302626 Reorder the terms: -2.7 + x = 3.562302626 Solving -2.7 + x = 3.562302626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.7' to each side of the equation. -2.7 + 2.7 + x = 3.562302626 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = 3.562302626 + 2.7 x = 3.562302626 + 2.7 Combine like terms: 3.562302626 + 2.7 = 6.262302626 x = 6.262302626 Simplifying x = 6.262302626Subproblem 2
x + -2.7 = -3.562302626 Simplifying x + -2.7 = -3.562302626 Reorder the terms: -2.7 + x = -3.562302626 Solving -2.7 + x = -3.562302626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.7' to each side of the equation. -2.7 + 2.7 + x = -3.562302626 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = -3.562302626 + 2.7 x = -3.562302626 + 2.7 Combine like terms: -3.562302626 + 2.7 = -0.862302626 x = -0.862302626 Simplifying x = -0.862302626Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.262302626, -0.862302626}
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