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Simplifying x2 + -11x + -11 = 9x + 4 Reorder the terms: -11 + -11x + x2 = 9x + 4 Reorder the terms: -11 + -11x + x2 = 4 + 9x Solving -11 + -11x + x2 = 4 + 9x Solving for variable 'x'. Reorder the terms: -11 + -4 + -11x + -9x + x2 = 4 + 9x + -4 + -9x Combine like terms: -11 + -4 = -15 -15 + -11x + -9x + x2 = 4 + 9x + -4 + -9x Combine like terms: -11x + -9x = -20x -15 + -20x + x2 = 4 + 9x + -4 + -9x Reorder the terms: -15 + -20x + x2 = 4 + -4 + 9x + -9x Combine like terms: 4 + -4 = 0 -15 + -20x + x2 = 0 + 9x + -9x -15 + -20x + x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -15 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -20x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -20x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -20x + x2 = 0 + 15 -20x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -20x + x2 = 15 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 15 + 100 Reorder the terms: 100 + -20x + x2 = 15 + 100 Combine like terms: 15 + 100 = 115 100 + -20x + x2 = 115 Factor a perfect square on the left side: (x + -10)(x + -10) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (x + -10) equal to 10.723805295 and -10.723805295.Subproblem 1
x + -10 = 10.723805295 Simplifying x + -10 = 10.723805295 Reorder the terms: -10 + x = 10.723805295 Solving -10 + x = 10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 10.723805295 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.723805295 + 10 x = 10.723805295 + 10 Combine like terms: 10.723805295 + 10 = 20.723805295 x = 20.723805295 Simplifying x = 20.723805295Subproblem 2
x + -10 = -10.723805295 Simplifying x + -10 = -10.723805295 Reorder the terms: -10 + x = -10.723805295 Solving -10 + x = -10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -10.723805295 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.723805295 + 10 x = -10.723805295 + 10 Combine like terms: -10.723805295 + 10 = -0.723805295 x = -0.723805295 Simplifying x = -0.723805295Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.723805295, -0.723805295}
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