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Simplifying 2x2 + 22x + -4 = 0 Reorder the terms: -4 + 22x + 2x2 = 0 Solving -4 + 22x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 11x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 11x + x2)' equal to zero and attempt to solve: Simplifying -2 + 11x + x2 = 0 Solving -2 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 11x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 11x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 11x + x2 = 0 + 2 11x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 11x + x2 = 2 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 = 2 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 2 + 30.25 Combine like terms: 2 + 30.25 = 32.25 30.25 + 11x + x2 = 32.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + 5.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x + 5.5 = 5.678908346 Simplifying x + 5.5 = 5.678908346 Reorder the terms: 5.5 + x = 5.678908346 Solving 5.5 + x = 5.678908346 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 = 5.678908346 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 5.678908346 + -5.5 x = 5.678908346 + -5.5 Combine like terms: 5.678908346 + -5.5 = 0.178908346 x = 0.178908346 Simplifying x = 0.178908346Subproblem 2
x + 5.5 = -5.678908346 Simplifying x + 5.5 = -5.678908346 Reorder the terms: 5.5 + x = -5.678908346 Solving 5.5 + x = -5.678908346 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 = -5.678908346 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -5.678908346 + -5.5 x = -5.678908346 + -5.5 Combine like terms: -5.678908346 + -5.5 = -11.178908346 x = -11.178908346 Simplifying x = -11.178908346Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.178908346, -11.178908346}Solution
x = {0.178908346, -11.178908346}
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