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Simplifying 6x2 + -66x + 24 = 0 Reorder the terms: 24 + -66x + 6x2 = 0 Solving 24 + -66x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(4 + -11x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(4 + -11x + x2)' equal to zero and attempt to solve: Simplifying 4 + -11x + x2 = 0 Solving 4 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -11x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -11x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -11x + x2 = 0 + -4 -11x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -11x + x2 = -4 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -4 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -4 + 30.25 Combine like terms: -4 + 30.25 = 26.25 30.25 + -11x + x2 = 26.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (x + -5.5) equal to 5.123475383 and -5.123475383.Subproblem 1
x + -5.5 = 5.123475383 Simplifying x + -5.5 = 5.123475383 Reorder the terms: -5.5 + x = 5.123475383 Solving -5.5 + x = 5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.123475383 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.123475383 + 5.5 x = 5.123475383 + 5.5 Combine like terms: 5.123475383 + 5.5 = 10.623475383 x = 10.623475383 Simplifying x = 10.623475383Subproblem 2
x + -5.5 = -5.123475383 Simplifying x + -5.5 = -5.123475383 Reorder the terms: -5.5 + x = -5.123475383 Solving -5.5 + x = -5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.123475383 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.123475383 + 5.5 x = -5.123475383 + 5.5 Combine like terms: -5.123475383 + 5.5 = 0.376524617 x = 0.376524617 Simplifying x = 0.376524617Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.623475383, 0.376524617}Solution
x = {10.623475383, 0.376524617}
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