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Simplifying 20x2 + 20x + 2 = 0 Reorder the terms: 2 + 20x + 20x2 = 0 Solving 2 + 20x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 10x + 10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 10x + 10x2)' equal to zero and attempt to solve: Simplifying 1 + 10x + 10x2 = 0 Solving 1 + 10x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.1 + x + x2 = 0.0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + x + -0.1 + x2 = 0.0 + -0.1 Reorder the terms: 0.1 + -0.1 + x + x2 = 0.0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x + x2 = 0.0 + -0.1 x + x2 = 0.0 + -0.1 Combine like terms: 0.0 + -0.1 = -0.1 x + x2 = -0.1 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = -0.1 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.1 + 0.25 Combine like terms: -0.1 + 0.25 = 0.15 1.25 + x2 = 0.15 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.15 Calculate the square root of the right side: 0.387298335 Break this problem into two subproblems by setting (x + 0.5) equal to 0.387298335 and -0.387298335.Subproblem 1
x + 0.5 = 0.387298335 Simplifying x + 0.5 = 0.387298335 Reorder the terms: 0.5 + x = 0.387298335 Solving 0.5 + x = 0.387298335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.387298335 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.387298335 + -0.5 x = 0.387298335 + -0.5 Combine like terms: 0.387298335 + -0.5 = -0.112701665 x = -0.112701665 Simplifying x = -0.112701665Subproblem 2
x + 0.5 = -0.387298335 Simplifying x + 0.5 = -0.387298335 Reorder the terms: 0.5 + x = -0.387298335 Solving 0.5 + x = -0.387298335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.387298335 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.387298335 + -0.5 x = -0.387298335 + -0.5 Combine like terms: -0.387298335 + -0.5 = -0.887298335 x = -0.887298335 Simplifying x = -0.887298335Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.112701665, -0.887298335}Solution
x = {-0.112701665, -0.887298335}
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