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Simplifying 45 = 5x + x2 + 6 Reorder the terms: 45 = 6 + 5x + x2 Solving 45 = 6 + 5x + x2 Solving for variable 'x'. Combine like terms: 45 + -6 = 39 39 + -5x + -1x2 = 6 + 5x + x2 + -6 + -5x + -1x2 Reorder the terms: 39 + -5x + -1x2 = 6 + -6 + 5x + -5x + x2 + -1x2 Combine like terms: 6 + -6 = 0 39 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 39 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 39 + -5x + -1x2 = 0 + x2 + -1x2 39 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 39 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -39 + 5x + x2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + 5x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 5x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 5x + x2 = 0 + 39 5x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 5x + x2 = 39 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 = 39 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 39 + 6.25 Combine like terms: 39 + 6.25 = 45.25 6.25 + 5x + x2 = 45.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (x + 2.5) equal to 6.726812024 and -6.726812024.Subproblem 1
x + 2.5 = 6.726812024 Simplifying x + 2.5 = 6.726812024 Reorder the terms: 2.5 + x = 6.726812024 Solving 2.5 + x = 6.726812024 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 = 6.726812024 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.726812024 + -2.5 x = 6.726812024 + -2.5 Combine like terms: 6.726812024 + -2.5 = 4.226812024 x = 4.226812024 Simplifying x = 4.226812024Subproblem 2
x + 2.5 = -6.726812024 Simplifying x + 2.5 = -6.726812024 Reorder the terms: 2.5 + x = -6.726812024 Solving 2.5 + x = -6.726812024 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 = -6.726812024 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.726812024 + -2.5 x = -6.726812024 + -2.5 Combine like terms: -6.726812024 + -2.5 = -9.226812024 x = -9.226812024 Simplifying x = -9.226812024Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.226812024, -9.226812024}
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