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Simplifying x2 + -9x + -5 = 23 Reorder the terms: -5 + -9x + x2 = 23 Solving -5 + -9x + x2 = 23 Solving for variable 'x'. Reorder the terms: -5 + -23 + -9x + x2 = 23 + -23 Combine like terms: -5 + -23 = -28 -28 + -9x + x2 = 23 + -23 Combine like terms: 23 + -23 = 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 = 11.446221995 x = 11.446221995 Simplifying x = 11.446221995Subproblem 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 = -2.446221995 x = -2.446221995 Simplifying x = -2.446221995Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.446221995, -2.446221995}
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