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Simplifying 2x2 + 22x + 8 = 0 Reorder the terms: 8 + 22x + 2x2 = 0 Solving 8 + 22x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 11x + x2) = 0 Ignore the factor 2.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 = -0.376524617 x = -0.376524617 Simplifying x = -0.376524617Subproblem 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 = -10.623475383 x = -10.623475383 Simplifying x = -10.623475383Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.376524617, -10.623475383}Solution
x = {-0.376524617, -10.623475383}
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