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Simplifying x2 + -6x + 9 = x + 45 Reorder the terms: 9 + -6x + x2 = x + 45 Reorder the terms: 9 + -6x + x2 = 45 + x Solving 9 + -6x + x2 = 45 + x Solving for variable 'x'. Reorder the terms: 9 + -45 + -6x + -1x + x2 = 45 + x + -45 + -1x Combine like terms: 9 + -45 = -36 -36 + -6x + -1x + x2 = 45 + x + -45 + -1x Combine like terms: -6x + -1x = -7x -36 + -7x + x2 = 45 + x + -45 + -1x Reorder the terms: -36 + -7x + x2 = 45 + -45 + x + -1x Combine like terms: 45 + -45 = 0 -36 + -7x + x2 = 0 + x + -1x -36 + -7x + x2 = x + -1x Combine like terms: x + -1x = 0 -36 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -7x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -7x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -7x + x2 = 0 + 36 -7x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -7x + x2 = 36 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 36 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 36 + 12.25 Combine like terms: 36 + 12.25 = 48.25 12.25 + -7x + x2 = 48.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + -3.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x + -3.5 = 6.946221995 Simplifying x + -3.5 = 6.946221995 Reorder the terms: -3.5 + x = 6.946221995 Solving -3.5 + x = 6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 6.946221995 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 6.946221995 + 3.5 x = 6.946221995 + 3.5 Combine like terms: 6.946221995 + 3.5 = 10.446221995 x = 10.446221995 Simplifying x = 10.446221995Subproblem 2
x + -3.5 = -6.946221995 Simplifying x + -3.5 = -6.946221995 Reorder the terms: -3.5 + x = -6.946221995 Solving -3.5 + x = -6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -6.946221995 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -6.946221995 + 3.5 x = -6.946221995 + 3.5 Combine like terms: -6.946221995 + 3.5 = -3.446221995 x = -3.446221995 Simplifying x = -3.446221995Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.446221995, -3.446221995}
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