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Simplifying (2x + 3)(2x + 6) = 5 Reorder the terms: (3 + 2x)(2x + 6) = 5 Reorder the terms: (3 + 2x)(6 + 2x) = 5 Multiply (3 + 2x) * (6 + 2x) (3(6 + 2x) + 2x * (6 + 2x)) = 5 ((6 * 3 + 2x * 3) + 2x * (6 + 2x)) = 5 ((18 + 6x) + 2x * (6 + 2x)) = 5 (18 + 6x + (6 * 2x + 2x * 2x)) = 5 (18 + 6x + (12x + 4x2)) = 5 Combine like terms: 6x + 12x = 18x (18 + 18x + 4x2) = 5 Solving 18 + 18x + 4x2 = 5 Solving for variable 'x'. Reorder the terms: 18 + -5 + 18x + 4x2 = 5 + -5 Combine like terms: 18 + -5 = 13 13 + 18x + 4x2 = 5 + -5 Combine like terms: 5 + -5 = 0 13 + 18x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + 4.5x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + 4.5x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + 4.5x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + 4.5x + x2 = 0 + -3.25 4.5x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 4.5x + x2 = -3.25 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = -3.25 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -3.25 + 5.0625 Combine like terms: -3.25 + 5.0625 = 1.8125 5.0625 + 4.5x + x2 = 1.8125 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 1.8125 Calculate the square root of the right side: 1.346291202 Break this problem into two subproblems by setting (x + 2.25) equal to 1.346291202 and -1.346291202.Subproblem 1
x + 2.25 = 1.346291202 Simplifying x + 2.25 = 1.346291202 Reorder the terms: 2.25 + x = 1.346291202 Solving 2.25 + x = 1.346291202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 1.346291202 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 1.346291202 + -2.25 x = 1.346291202 + -2.25 Combine like terms: 1.346291202 + -2.25 = -0.903708798 x = -0.903708798 Simplifying x = -0.903708798Subproblem 2
x + 2.25 = -1.346291202 Simplifying x + 2.25 = -1.346291202 Reorder the terms: 2.25 + x = -1.346291202 Solving 2.25 + x = -1.346291202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -1.346291202 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -1.346291202 + -2.25 x = -1.346291202 + -2.25 Combine like terms: -1.346291202 + -2.25 = -3.596291202 x = -3.596291202 Simplifying x = -3.596291202Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.903708798, -3.596291202}
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