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Simplifying 20x2 + 2 = 20x Reorder the terms: 2 + 20x2 = 20x Solving 2 + 20x2 = 20x Solving for variable 'x'. Reorder the terms: 2 + -20x + 20x2 = 20x + -20x Combine like terms: 20x + -20x = 0 2 + -20x + 20x2 = 0 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 + -1x + x2 = 0.0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + -1x + -0.1 + x2 = 0.0 + -0.1 Reorder the terms: 0.1 + -0.1 + -1x + x2 = 0.0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + -1x + x2 = 0.0 + -0.1 -1x + x2 = 0.0 + -0.1 Combine like terms: 0.0 + -0.1 = -0.1 -1x + x2 = -0.1 The x term is -1x. 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. -1x + 0.25 + x2 = -0.1 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.1 + 0.25 Combine like terms: -0.1 + 0.25 = 0.15 0.25 + -1x + 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 = 0.887298335 x = 0.887298335 Simplifying x = 0.887298335Subproblem 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 = 0.112701665 x = 0.112701665 Simplifying x = 0.112701665Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.887298335, 0.112701665}Solution
x = {0.887298335, 0.112701665}
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