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Simplifying 0 = 5x2 + -20x + 5 Reorder the terms: 0 = 5 + -20x + 5x2 Solving 0 = 5 + -20x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + 20x + -5x2 = 5 + -20x + 5x2 + -5 + 20x + -5x2 Reorder the terms: -5 + 20x + -5x2 = 5 + -5 + -20x + 20x + 5x2 + -5x2 Combine like terms: 5 + -5 = 0 -5 + 20x + -5x2 = 0 + -20x + 20x + 5x2 + -5x2 -5 + 20x + -5x2 = -20x + 20x + 5x2 + -5x2 Combine like terms: -20x + 20x = 0 -5 + 20x + -5x2 = 0 + 5x2 + -5x2 -5 + 20x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -5 + 20x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-1 + 4x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying -1 + 4x + -1x2 = 0 Solving -1 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -4x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -4x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x + x2 = 0 + -1 -4x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4x + x2 = -1 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 = -1 + 4 Reorder the terms: 4 + -4x + x2 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + -4x + x2 = 3 Factor a perfect square on the left side: (x + -2)(x + -2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -2) equal to 1.732050808 and -1.732050808.Subproblem 1
x + -2 = 1.732050808 Simplifying x + -2 = 1.732050808 Reorder the terms: -2 + x = 1.732050808 Solving -2 + x = 1.732050808 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 = 1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.732050808 + 2 x = 1.732050808 + 2 Combine like terms: 1.732050808 + 2 = 3.732050808 x = 3.732050808 Simplifying x = 3.732050808Subproblem 2
x + -2 = -1.732050808 Simplifying x + -2 = -1.732050808 Reorder the terms: -2 + x = -1.732050808 Solving -2 + x = -1.732050808 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 = -1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.732050808 + 2 x = -1.732050808 + 2 Combine like terms: -1.732050808 + 2 = 0.267949192 x = 0.267949192 Simplifying x = 0.267949192Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.732050808, 0.267949192}Solution
x = {3.732050808, 0.267949192}
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