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Simplifying (2x + 6)(2x + 4) = 55.25 Reorder the terms: (6 + 2x)(2x + 4) = 55.25 Reorder the terms: (6 + 2x)(4 + 2x) = 55.25 Multiply (6 + 2x) * (4 + 2x) (6(4 + 2x) + 2x * (4 + 2x)) = 55.25 ((4 * 6 + 2x * 6) + 2x * (4 + 2x)) = 55.25 ((24 + 12x) + 2x * (4 + 2x)) = 55.25 (24 + 12x + (4 * 2x + 2x * 2x)) = 55.25 (24 + 12x + (8x + 4x2)) = 55.25 Combine like terms: 12x + 8x = 20x (24 + 20x + 4x2) = 55.25 Solving 24 + 20x + 4x2 = 55.25 Solving for variable 'x'. Reorder the terms: 24 + -55.25 + 20x + 4x2 = 55.25 + -55.25 Combine like terms: 24 + -55.25 = -31.25 -31.25 + 20x + 4x2 = 55.25 + -55.25 Combine like terms: 55.25 + -55.25 = 0.00 -31.25 + 20x + 4x2 = 0.00 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.8125 + 5x + x2 = 0.00 Move the constant term to the right: Add '7.8125' to each side of the equation. -7.8125 + 5x + 7.8125 + x2 = 0.00 + 7.8125 Reorder the terms: -7.8125 + 7.8125 + 5x + x2 = 0.00 + 7.8125 Combine like terms: -7.8125 + 7.8125 = 0.0000 0.0000 + 5x + x2 = 0.00 + 7.8125 5x + x2 = 0.00 + 7.8125 Combine like terms: 0.00 + 7.8125 = 7.8125 5x + x2 = 7.8125 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 7.8125 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 7.8125 + 6.25 Combine like terms: 7.8125 + 6.25 = 14.0625 6.25 + 5x + x2 = 14.0625 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 14.0625 Calculate the square root of the right side: 3.75 Break this problem into two subproblems by setting (x + 2.5) equal to 3.75 and -3.75.Subproblem 1
x + 2.5 = 3.75 Simplifying x + 2.5 = 3.75 Reorder the terms: 2.5 + x = 3.75 Solving 2.5 + x = 3.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.75 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.75 + -2.5 x = 3.75 + -2.5 Combine like terms: 3.75 + -2.5 = 1.25 x = 1.25 Simplifying x = 1.25Subproblem 2
x + 2.5 = -3.75 Simplifying x + 2.5 = -3.75 Reorder the terms: 2.5 + x = -3.75 Solving 2.5 + x = -3.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.75 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.75 + -2.5 x = -3.75 + -2.5 Combine like terms: -3.75 + -2.5 = -6.25 x = -6.25 Simplifying x = -6.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.25, -6.25}
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