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Simplifying 20x2 + -80x + 4 = 0 Reorder the terms: 4 + -80x + 20x2 = 0 Solving 4 + -80x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + -20x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -20x + 5x2)' equal to zero and attempt to solve: Simplifying 1 + -20x + 5x2 = 0 Solving 1 + -20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -4x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -4x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -4x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -4x + x2 = 0 + -0.2 -4x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -4x + x2 = -0.2 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -0.2 + 4 Reorder the terms: 4 + -4x + x2 = -0.2 + 4 Combine like terms: -0.2 + 4 = 3.8 4 + -4x + x2 = 3.8 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.8 Calculate the square root of the right side: 1.949358869 Break this problem into two subproblems by setting (x + -2) equal to 1.949358869 and -1.949358869.Subproblem 1
x + -2 = 1.949358869 Simplifying x + -2 = 1.949358869 Reorder the terms: -2 + x = 1.949358869 Solving -2 + x = 1.949358869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.949358869 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.949358869 + 2 x = 1.949358869 + 2 Combine like terms: 1.949358869 + 2 = 3.949358869 x = 3.949358869 Simplifying x = 3.949358869Subproblem 2
x + -2 = -1.949358869 Simplifying x + -2 = -1.949358869 Reorder the terms: -2 + x = -1.949358869 Solving -2 + x = -1.949358869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.949358869 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.949358869 + 2 x = -1.949358869 + 2 Combine like terms: -1.949358869 + 2 = 0.050641131 x = 0.050641131 Simplifying x = 0.050641131Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.949358869, 0.050641131}Solution
x = {3.949358869, 0.050641131}
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