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Simplifying 2x2 + 18x + 2 = 0 Reorder the terms: 2 + 18x + 2x2 = 0 Solving 2 + 18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 9x + x2)' equal to zero and attempt to solve: Simplifying 1 + 9x + x2 = 0 Solving 1 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 9x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 9x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 9x + x2 = 0 + -1 9x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 9x + x2 = -1 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -1 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -1 + 20.25 Combine like terms: -1 + 20.25 = 19.25 20.25 + 9x + x2 = 19.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + 4.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x + 4.5 = 4.387482194 Simplifying x + 4.5 = 4.387482194 Reorder the terms: 4.5 + x = 4.387482194 Solving 4.5 + x = 4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 4.387482194 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.387482194 + -4.5 x = 4.387482194 + -4.5 Combine like terms: 4.387482194 + -4.5 = -0.112517806 x = -0.112517806 Simplifying x = -0.112517806Subproblem 2
x + 4.5 = -4.387482194 Simplifying x + 4.5 = -4.387482194 Reorder the terms: 4.5 + x = -4.387482194 Solving 4.5 + x = -4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -4.387482194 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.387482194 + -4.5 x = -4.387482194 + -4.5 Combine like terms: -4.387482194 + -4.5 = -8.887482194 x = -8.887482194 Simplifying x = -8.887482194Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.112517806, -8.887482194}Solution
x = {-0.112517806, -8.887482194}
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