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Simplifying 2x2 + 22x + 6 = 0 Reorder the terms: 6 + 22x + 2x2 = 0 Solving 6 + 22x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 11x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 11x + x2)' equal to zero and attempt to solve: Simplifying 3 + 11x + x2 = 0 Solving 3 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 11x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 11x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 11x + x2 = 0 + -3 11x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 11x + x2 = -3 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 = -3 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -3 + 30.25 Combine like terms: -3 + 30.25 = 27.25 30.25 + 11x + x2 = 27.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + 5.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + 5.5 = 5.220153254 Simplifying x + 5.5 = 5.220153254 Reorder the terms: 5.5 + x = 5.220153254 Solving 5.5 + x = 5.220153254 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 = 5.220153254 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 5.220153254 + -5.5 x = 5.220153254 + -5.5 Combine like terms: 5.220153254 + -5.5 = -0.279846746 x = -0.279846746 Simplifying x = -0.279846746Subproblem 2
x + 5.5 = -5.220153254 Simplifying x + 5.5 = -5.220153254 Reorder the terms: 5.5 + x = -5.220153254 Solving 5.5 + x = -5.220153254 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 = -5.220153254 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -5.220153254 + -5.5 x = -5.220153254 + -5.5 Combine like terms: -5.220153254 + -5.5 = -10.720153254 x = -10.720153254 Simplifying x = -10.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.279846746, -10.720153254}Solution
x = {-0.279846746, -10.720153254}
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