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Simplifying 2(5x + -3) * 3(2x + -1) = 9 Reorder the terms: 2(-3 + 5x) * 3(2x + -1) = 9 Reorder the terms: 2(-3 + 5x) * 3(-1 + 2x) = 9 Reorder the terms for easier multiplication: 2 * 3(-3 + 5x)(-1 + 2x) = 9 Multiply 2 * 3 6(-3 + 5x)(-1 + 2x) = 9 Multiply (-3 + 5x) * (-1 + 2x) 6(-3(-1 + 2x) + 5x * (-1 + 2x)) = 9 6((-1 * -3 + 2x * -3) + 5x * (-1 + 2x)) = 9 6((3 + -6x) + 5x * (-1 + 2x)) = 9 6(3 + -6x + (-1 * 5x + 2x * 5x)) = 9 6(3 + -6x + (-5x + 10x2)) = 9 Combine like terms: -6x + -5x = -11x 6(3 + -11x + 10x2) = 9 (3 * 6 + -11x * 6 + 10x2 * 6) = 9 (18 + -66x + 60x2) = 9 Solving 18 + -66x + 60x2 = 9 Solving for variable 'x'. Reorder the terms: 18 + -9 + -66x + 60x2 = 9 + -9 Combine like terms: 18 + -9 = 9 9 + -66x + 60x2 = 9 + -9 Combine like terms: 9 + -9 = 0 9 + -66x + 60x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -22x + 20x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -22x + 20x2)' equal to zero and attempt to solve: Simplifying 3 + -22x + 20x2 = 0 Solving 3 + -22x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.15 + -1.1x + x2 = 0.0 Move the constant term to the right: Add '-0.15' to each side of the equation. 0.15 + -1.1x + -0.15 + x2 = 0.0 + -0.15 Reorder the terms: 0.15 + -0.15 + -1.1x + x2 = 0.0 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + -1.1x + x2 = 0.0 + -0.15 -1.1x + x2 = 0.0 + -0.15 Combine like terms: 0.0 + -0.15 = -0.15 -1.1x + x2 = -0.15 The x term is -1.1x. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1x + 0.3025 + x2 = -0.15 + 0.3025 Reorder the terms: 0.3025 + -1.1x + x2 = -0.15 + 0.3025 Combine like terms: -0.15 + 0.3025 = 0.1525 0.3025 + -1.1x + x2 = 0.1525 Factor a perfect square on the left side: (x + -0.55)(x + -0.55) = 0.1525 Calculate the square root of the right side: 0.390512484 Break this problem into two subproblems by setting (x + -0.55) equal to 0.390512484 and -0.390512484.Subproblem 1
x + -0.55 = 0.390512484 Simplifying x + -0.55 = 0.390512484 Reorder the terms: -0.55 + x = 0.390512484 Solving -0.55 + x = 0.390512484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = 0.390512484 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = 0.390512484 + 0.55 x = 0.390512484 + 0.55 Combine like terms: 0.390512484 + 0.55 = 0.940512484 x = 0.940512484 Simplifying x = 0.940512484Subproblem 2
x + -0.55 = -0.390512484 Simplifying x + -0.55 = -0.390512484 Reorder the terms: -0.55 + x = -0.390512484 Solving -0.55 + x = -0.390512484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = -0.390512484 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = -0.390512484 + 0.55 x = -0.390512484 + 0.55 Combine like terms: -0.390512484 + 0.55 = 0.159487516 x = 0.159487516 Simplifying x = 0.159487516Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.940512484, 0.159487516}Solution
x = {0.940512484, 0.159487516}
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