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Simplifying 5x(x + 9) = 48 Reorder the terms: 5x(9 + x) = 48 (9 * 5x + x * 5x) = 48 (45x + 5x2) = 48 Solving 45x + 5x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + 45x + 5x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + 45x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.6 + 9x + x2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + 9x + 9.6 + x2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + 9x + x2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + 9x + x2 = 0 + 9.6 9x + x2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 9x + x2 = 9.6 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 = 9.6 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 9.6 + 20.25 Combine like terms: 9.6 + 20.25 = 29.85 20.25 + 9x + x2 = 29.85 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 29.85 Calculate the square root of the right side: 5.463515352 Break this problem into two subproblems by setting (x + 4.5) equal to 5.463515352 and -5.463515352.Subproblem 1
x + 4.5 = 5.463515352 Simplifying x + 4.5 = 5.463515352 Reorder the terms: 4.5 + x = 5.463515352 Solving 4.5 + x = 5.463515352 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 = 5.463515352 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.463515352 + -4.5 x = 5.463515352 + -4.5 Combine like terms: 5.463515352 + -4.5 = 0.963515352 x = 0.963515352 Simplifying x = 0.963515352Subproblem 2
x + 4.5 = -5.463515352 Simplifying x + 4.5 = -5.463515352 Reorder the terms: 4.5 + x = -5.463515352 Solving 4.5 + x = -5.463515352 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 = -5.463515352 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.463515352 + -4.5 x = -5.463515352 + -4.5 Combine like terms: -5.463515352 + -4.5 = -9.963515352 x = -9.963515352 Simplifying x = -9.963515352Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.963515352, -9.963515352}
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