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Simplifying (x + 5)(x) = 43 Reorder the terms: (5 + x)(x) = 43 Reorder the terms for easier multiplication: x(5 + x) = 43 (5 * x + x * x) = 43 (5x + x2) = 43 Solving 5x + x2 = 43 Solving for variable 'x'. Reorder the terms: -43 + 5x + x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 5x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + 5x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 5x + x2 = 0 + 43 5x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 5x + x2 = 43 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 = 43 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 43 + 6.25 Combine like terms: 43 + 6.25 = 49.25 6.25 + 5x + x2 = 49.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (x + 2.5) equal to 7.017834424 and -7.017834424.Subproblem 1
x + 2.5 = 7.017834424 Simplifying x + 2.5 = 7.017834424 Reorder the terms: 2.5 + x = 7.017834424 Solving 2.5 + x = 7.017834424 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 = 7.017834424 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 7.017834424 + -2.5 x = 7.017834424 + -2.5 Combine like terms: 7.017834424 + -2.5 = 4.517834424 x = 4.517834424 Simplifying x = 4.517834424Subproblem 2
x + 2.5 = -7.017834424 Simplifying x + 2.5 = -7.017834424 Reorder the terms: 2.5 + x = -7.017834424 Solving 2.5 + x = -7.017834424 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 = -7.017834424 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -7.017834424 + -2.5 x = -7.017834424 + -2.5 Combine like terms: -7.017834424 + -2.5 = -9.517834424 x = -9.517834424 Simplifying x = -9.517834424Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.517834424, -9.517834424}
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