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Simplifying (4x + 2)(x + 5) = 48 Reorder the terms: (2 + 4x)(x + 5) = 48 Reorder the terms: (2 + 4x)(5 + x) = 48 Multiply (2 + 4x) * (5 + x) (2(5 + x) + 4x * (5 + x)) = 48 ((5 * 2 + x * 2) + 4x * (5 + x)) = 48 ((10 + 2x) + 4x * (5 + x)) = 48 (10 + 2x + (5 * 4x + x * 4x)) = 48 (10 + 2x + (20x + 4x2)) = 48 Combine like terms: 2x + 20x = 22x (10 + 22x + 4x2) = 48 Solving 10 + 22x + 4x2 = 48 Solving for variable 'x'. Reorder the terms: 10 + -48 + 22x + 4x2 = 48 + -48 Combine like terms: 10 + -48 = -38 -38 + 22x + 4x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -38 + 22x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + 11x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + 11x + 2x2)' equal to zero and attempt to solve: Simplifying -19 + 11x + 2x2 = 0 Solving -19 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + 5.5x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 5.5x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 5.5x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 5.5x + x2 = 0 + 9.5 5.5x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 5.5x + x2 = 9.5 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 9.5 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 9.5 + 7.5625 Combine like terms: 9.5 + 7.5625 = 17.0625 7.5625 + 5.5x + x2 = 17.0625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 17.0625 Calculate the square root of the right side: 4.13067791 Break this problem into two subproblems by setting (x + 2.75) equal to 4.13067791 and -4.13067791.Subproblem 1
x + 2.75 = 4.13067791 Simplifying x + 2.75 = 4.13067791 Reorder the terms: 2.75 + x = 4.13067791 Solving 2.75 + x = 4.13067791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 4.13067791 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 4.13067791 + -2.75 x = 4.13067791 + -2.75 Combine like terms: 4.13067791 + -2.75 = 1.38067791 x = 1.38067791 Simplifying x = 1.38067791Subproblem 2
x + 2.75 = -4.13067791 Simplifying x + 2.75 = -4.13067791 Reorder the terms: 2.75 + x = -4.13067791 Solving 2.75 + x = -4.13067791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -4.13067791 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -4.13067791 + -2.75 x = -4.13067791 + -2.75 Combine like terms: -4.13067791 + -2.75 = -6.88067791 x = -6.88067791 Simplifying x = -6.88067791Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.38067791, -6.88067791}Solution
x = {1.38067791, -6.88067791}
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