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Simplifying (x + 5)(x + 4) = 52 Reorder the terms: (5 + x)(x + 4) = 52 Reorder the terms: (5 + x)(4 + x) = 52 Multiply (5 + x) * (4 + x) (5(4 + x) + x(4 + x)) = 52 ((4 * 5 + x * 5) + x(4 + x)) = 52 ((20 + 5x) + x(4 + x)) = 52 (20 + 5x + (4 * x + x * x)) = 52 (20 + 5x + (4x + x2)) = 52 Combine like terms: 5x + 4x = 9x (20 + 9x + x2) = 52 Solving 20 + 9x + x2 = 52 Solving for variable 'x'. Reorder the terms: 20 + -52 + 9x + x2 = 52 + -52 Combine like terms: 20 + -52 = -32 -32 + 9x + x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -32 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 9x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 9x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 9x + x2 = 0 + 32 9x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 9x + x2 = 32 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 32 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 32 + 20.25 Combine like terms: 32 + 20.25 = 52.25 20.25 + 9x + x2 = 52.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + 4.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + 4.5 = 7.228416147 Simplifying x + 4.5 = 7.228416147 Reorder the terms: 4.5 + x = 7.228416147 Solving 4.5 + x = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 7.228416147 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 7.228416147 + -4.5 x = 7.228416147 + -4.5 Combine like terms: 7.228416147 + -4.5 = 2.728416147 x = 2.728416147 Simplifying x = 2.728416147Subproblem 2
x + 4.5 = -7.228416147 Simplifying x + 4.5 = -7.228416147 Reorder the terms: 4.5 + x = -7.228416147 Solving 4.5 + x = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -7.228416147 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -7.228416147 + -4.5 x = -7.228416147 + -4.5 Combine like terms: -7.228416147 + -4.5 = -11.728416147 x = -11.728416147 Simplifying x = -11.728416147Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.728416147, -11.728416147}
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