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Simplifying 0 = x2 + 21x + 11 Reorder the terms: 0 = 11 + 21x + x2 Solving 0 = 11 + 21x + x2 Solving for variable 'x'. Combine like terms: 0 + -11 = -11 -11 + -21x + -1x2 = 11 + 21x + x2 + -11 + -21x + -1x2 Reorder the terms: -11 + -21x + -1x2 = 11 + -11 + 21x + -21x + x2 + -1x2 Combine like terms: 11 + -11 = 0 -11 + -21x + -1x2 = 0 + 21x + -21x + x2 + -1x2 -11 + -21x + -1x2 = 21x + -21x + x2 + -1x2 Combine like terms: 21x + -21x = 0 -11 + -21x + -1x2 = 0 + x2 + -1x2 -11 + -21x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -11 + -21x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 21x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 21x + x2)' equal to zero and attempt to solve: Simplifying 11 + 21x + x2 = 0 Solving 11 + 21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 21x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 21x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 21x + x2 = 0 + -11 21x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 21x + x2 = -11 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = -11 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -11 + 110.25 Combine like terms: -11 + 110.25 = 99.25 110.25 + 21x + x2 = 99.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 99.25 Calculate the square root of the right side: 9.962429423 Break this problem into two subproblems by setting (x + 10.5) equal to 9.962429423 and -9.962429423.Subproblem 1
x + 10.5 = 9.962429423 Simplifying x + 10.5 = 9.962429423 Reorder the terms: 10.5 + x = 9.962429423 Solving 10.5 + x = 9.962429423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 9.962429423 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 9.962429423 + -10.5 x = 9.962429423 + -10.5 Combine like terms: 9.962429423 + -10.5 = -0.537570577 x = -0.537570577 Simplifying x = -0.537570577Subproblem 2
x + 10.5 = -9.962429423 Simplifying x + 10.5 = -9.962429423 Reorder the terms: 10.5 + x = -9.962429423 Solving 10.5 + x = -9.962429423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -9.962429423 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -9.962429423 + -10.5 x = -9.962429423 + -10.5 Combine like terms: -9.962429423 + -10.5 = -20.462429423 x = -20.462429423 Simplifying x = -20.462429423Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.537570577, -20.462429423}Solution
x = {-0.537570577, -20.462429423}
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