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Simplifying (4x + 9)(4x + 9) = 52 Reorder the terms: (9 + 4x)(4x + 9) = 52 Reorder the terms: (9 + 4x)(9 + 4x) = 52 Multiply (9 + 4x) * (9 + 4x) (9(9 + 4x) + 4x * (9 + 4x)) = 52 ((9 * 9 + 4x * 9) + 4x * (9 + 4x)) = 52 ((81 + 36x) + 4x * (9 + 4x)) = 52 (81 + 36x + (9 * 4x + 4x * 4x)) = 52 (81 + 36x + (36x + 16x2)) = 52 Combine like terms: 36x + 36x = 72x (81 + 72x + 16x2) = 52 Solving 81 + 72x + 16x2 = 52 Solving for variable 'x'. Reorder the terms: 81 + -52 + 72x + 16x2 = 52 + -52 Combine like terms: 81 + -52 = 29 29 + 72x + 16x2 = 52 + -52 Combine like terms: 52 + -52 = 0 29 + 72x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.8125 + 4.5x + x2 = 0 Move the constant term to the right: Add '-1.8125' to each side of the equation. 1.8125 + 4.5x + -1.8125 + x2 = 0 + -1.8125 Reorder the terms: 1.8125 + -1.8125 + 4.5x + x2 = 0 + -1.8125 Combine like terms: 1.8125 + -1.8125 = 0.0000 0.0000 + 4.5x + x2 = 0 + -1.8125 4.5x + x2 = 0 + -1.8125 Combine like terms: 0 + -1.8125 = -1.8125 4.5x + x2 = -1.8125 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 = -1.8125 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -1.8125 + 5.0625 Combine like terms: -1.8125 + 5.0625 = 3.25 5.0625 + 4.5x + x2 = 3.25 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 2.25) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 2.25 = 1.802775638 Simplifying x + 2.25 = 1.802775638 Reorder the terms: 2.25 + x = 1.802775638 Solving 2.25 + x = 1.802775638 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 = 1.802775638 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 1.802775638 + -2.25 x = 1.802775638 + -2.25 Combine like terms: 1.802775638 + -2.25 = -0.447224362 x = -0.447224362 Simplifying x = -0.447224362Subproblem 2
x + 2.25 = -1.802775638 Simplifying x + 2.25 = -1.802775638 Reorder the terms: 2.25 + x = -1.802775638 Solving 2.25 + x = -1.802775638 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 = -1.802775638 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -1.802775638 + -2.25 x = -1.802775638 + -2.25 Combine like terms: -1.802775638 + -2.25 = -4.052775638 x = -4.052775638 Simplifying x = -4.052775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.447224362, -4.052775638}
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