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Simplifying x2 + 6x + -23 = 5 + -3x Reorder the terms: -23 + 6x + x2 = 5 + -3x Solving -23 + 6x + x2 = 5 + -3x Solving for variable 'x'. Reorder the terms: -23 + -5 + 6x + 3x + x2 = 5 + -3x + -5 + 3x Combine like terms: -23 + -5 = -28 -28 + 6x + 3x + x2 = 5 + -3x + -5 + 3x Combine like terms: 6x + 3x = 9x -28 + 9x + x2 = 5 + -3x + -5 + 3x Reorder the terms: -28 + 9x + x2 = 5 + -5 + -3x + 3x Combine like terms: 5 + -5 = 0 -28 + 9x + x2 = 0 + -3x + 3x -28 + 9x + x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -28 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 9x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 9x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 9x + x2 = 0 + 28 9x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 9x + x2 = 28 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 = 28 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 28 + 20.25 Combine like terms: 28 + 20.25 = 48.25 20.25 + 9x + x2 = 48.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + 4.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x + 4.5 = 6.946221995 Simplifying x + 4.5 = 6.946221995 Reorder the terms: 4.5 + x = 6.946221995 Solving 4.5 + x = 6.946221995 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 = 6.946221995 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 6.946221995 + -4.5 x = 6.946221995 + -4.5 Combine like terms: 6.946221995 + -4.5 = 2.446221995 x = 2.446221995 Simplifying x = 2.446221995Subproblem 2
x + 4.5 = -6.946221995 Simplifying x + 4.5 = -6.946221995 Reorder the terms: 4.5 + x = -6.946221995 Solving 4.5 + x = -6.946221995 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 = -6.946221995 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -6.946221995 + -4.5 x = -6.946221995 + -4.5 Combine like terms: -6.946221995 + -4.5 = -11.446221995 x = -11.446221995 Simplifying x = -11.446221995Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.446221995, -11.446221995}
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