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Simplifying 4x(x2 + -21x + 11) = 0 Reorder the terms: 4x(11 + -21x + x2) = 0 (11 * 4x + -21x * 4x + x2 * 4x) = 0 (44x + -84x2 + 4x3) = 0 Solving 44x + -84x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(11 + -21x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
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 = 20.462429423 x = 20.462429423 Simplifying x = 20.462429423Subproblem 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 = 0.537570577 x = 0.537570577 Simplifying x = 0.537570577Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.462429423, 0.537570577}Solution
x = {0, 20.462429423, 0.537570577}
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