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Simplifying x2 + -9x = x + -22 Reorder the terms: -9x + x2 = x + -22 Reorder the terms: -9x + x2 = -22 + x Solving -9x + x2 = -22 + x Solving for variable 'x'. Reorder the terms: 22 + -9x + -1x + x2 = -22 + x + 22 + -1x Combine like terms: -9x + -1x = -10x 22 + -10x + x2 = -22 + x + 22 + -1x Reorder the terms: 22 + -10x + x2 = -22 + 22 + x + -1x Combine like terms: -22 + 22 = 0 22 + -10x + x2 = 0 + x + -1x 22 + -10x + x2 = x + -1x Combine like terms: x + -1x = 0 22 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + -10x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + -10x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -10x + x2 = 0 + -22 -10x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 -10x + x2 = -22 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -22 + 25 Reorder the terms: 25 + -10x + x2 = -22 + 25 Combine like terms: -22 + 25 = 3 25 + -10x + x2 = 3 Factor a perfect square on the left side: (x + -5)(x + -5) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -5) equal to 1.732050808 and -1.732050808.Subproblem 1
x + -5 = 1.732050808 Simplifying x + -5 = 1.732050808 Reorder the terms: -5 + x = 1.732050808 Solving -5 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 1.732050808 + 5 Combine like terms: -5 + 5 = 0 0 + x = 1.732050808 + 5 x = 1.732050808 + 5 Combine like terms: 1.732050808 + 5 = 6.732050808 x = 6.732050808 Simplifying x = 6.732050808Subproblem 2
x + -5 = -1.732050808 Simplifying x + -5 = -1.732050808 Reorder the terms: -5 + x = -1.732050808 Solving -5 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -1.732050808 + 5 Combine like terms: -5 + 5 = 0 0 + x = -1.732050808 + 5 x = -1.732050808 + 5 Combine like terms: -1.732050808 + 5 = 3.267949192 x = 3.267949192 Simplifying x = 3.267949192Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.732050808, 3.267949192}
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