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Simplifying (6x + 5)(2x + -1) = 22x + -9 Reorder the terms: (5 + 6x)(2x + -1) = 22x + -9 Reorder the terms: (5 + 6x)(-1 + 2x) = 22x + -9 Multiply (5 + 6x) * (-1 + 2x) (5(-1 + 2x) + 6x * (-1 + 2x)) = 22x + -9 ((-1 * 5 + 2x * 5) + 6x * (-1 + 2x)) = 22x + -9 ((-5 + 10x) + 6x * (-1 + 2x)) = 22x + -9 (-5 + 10x + (-1 * 6x + 2x * 6x)) = 22x + -9 (-5 + 10x + (-6x + 12x2)) = 22x + -9 Combine like terms: 10x + -6x = 4x (-5 + 4x + 12x2) = 22x + -9 Reorder the terms: -5 + 4x + 12x2 = -9 + 22x Solving -5 + 4x + 12x2 = -9 + 22x Solving for variable 'x'. Reorder the terms: -5 + 9 + 4x + -22x + 12x2 = -9 + 22x + 9 + -22x Combine like terms: -5 + 9 = 4 4 + 4x + -22x + 12x2 = -9 + 22x + 9 + -22x Combine like terms: 4x + -22x = -18x 4 + -18x + 12x2 = -9 + 22x + 9 + -22x Reorder the terms: 4 + -18x + 12x2 = -9 + 9 + 22x + -22x Combine like terms: -9 + 9 = 0 4 + -18x + 12x2 = 0 + 22x + -22x 4 + -18x + 12x2 = 22x + -22x Combine like terms: 22x + -22x = 0 4 + -18x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -9x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -9x + 6x2)' equal to zero and attempt to solve: Simplifying 2 + -9x + 6x2 = 0 Solving 2 + -9x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.3333333333 + -1.5x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -1.5x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -1.5x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -1.5x + x2 = 0 + -0.3333333333 -1.5x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -1.5x + x2 = -0.3333333333 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -0.3333333333 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -0.3333333333 + 0.5625 Combine like terms: -0.3333333333 + 0.5625 = 0.2291666667 0.5625 + -1.5x + x2 = 0.2291666667 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.2291666667 Calculate the square root of the right side: 0.478713554 Break this problem into two subproblems by setting (x + -0.75) equal to 0.478713554 and -0.478713554.Subproblem 1
x + -0.75 = 0.478713554 Simplifying x + -0.75 = 0.478713554 Reorder the terms: -0.75 + x = 0.478713554 Solving -0.75 + x = 0.478713554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.478713554 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.478713554 + 0.75 x = 0.478713554 + 0.75 Combine like terms: 0.478713554 + 0.75 = 1.228713554 x = 1.228713554 Simplifying x = 1.228713554Subproblem 2
x + -0.75 = -0.478713554 Simplifying x + -0.75 = -0.478713554 Reorder the terms: -0.75 + x = -0.478713554 Solving -0.75 + x = -0.478713554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.478713554 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.478713554 + 0.75 x = -0.478713554 + 0.75 Combine like terms: -0.478713554 + 0.75 = 0.271286446 x = 0.271286446 Simplifying x = 0.271286446Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.228713554, 0.271286446}Solution
x = {1.228713554, 0.271286446}
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