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Simplifying 2(5x2 + -20x + 4) = 0 Reorder the terms: 2(4 + -20x + 5x2) = 0 (4 * 2 + -20x * 2 + 5x2 * 2) = 0 (8 + -40x + 10x2) = 0 Solving 8 + -40x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -20x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -20x + 5x2)' equal to zero and attempt to solve: Simplifying 4 + -20x + 5x2 = 0 Solving 4 + -20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -4x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -4x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -4x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -4x + x2 = 0 + -0.8 -4x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -4x + x2 = -0.8 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 = -0.8 + 4 Reorder the terms: 4 + -4x + x2 = -0.8 + 4 Combine like terms: -0.8 + 4 = 3.2 4 + -4x + x2 = 3.2 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.2 Calculate the square root of the right side: 1.788854382 Break this problem into two subproblems by setting (x + -2) equal to 1.788854382 and -1.788854382.Subproblem 1
x + -2 = 1.788854382 Simplifying x + -2 = 1.788854382 Reorder the terms: -2 + x = 1.788854382 Solving -2 + x = 1.788854382 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 = 1.788854382 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.788854382 + 2 x = 1.788854382 + 2 Combine like terms: 1.788854382 + 2 = 3.788854382 x = 3.788854382 Simplifying x = 3.788854382Subproblem 2
x + -2 = -1.788854382 Simplifying x + -2 = -1.788854382 Reorder the terms: -2 + x = -1.788854382 Solving -2 + x = -1.788854382 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 = -1.788854382 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.788854382 + 2 x = -1.788854382 + 2 Combine like terms: -1.788854382 + 2 = 0.211145618 x = 0.211145618 Simplifying x = 0.211145618Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.788854382, 0.211145618}Solution
x = {3.788854382, 0.211145618}
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