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Simplifying 2(4x2 + 20x + -5) = 0 Reorder the terms: 2(-5 + 20x + 4x2) = 0 (-5 * 2 + 20x * 2 + 4x2 * 2) = 0 (-10 + 40x + 8x2) = 0 Solving -10 + 40x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 20x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 20x + 4x2)' equal to zero and attempt to solve: Simplifying -5 + 20x + 4x2 = 0 Solving -5 + 20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 5x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 5x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 5x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 5x + x2 = 0 + 1.25 5x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 5x + x2 = 1.25 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 1.25 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1.25 + 6.25 Combine like terms: 1.25 + 6.25 = 7.5 6.25 + 5x + x2 = 7.5 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (x + 2.5) equal to 2.738612788 and -2.738612788.Subproblem 1
x + 2.5 = 2.738612788 Simplifying x + 2.5 = 2.738612788 Reorder the terms: 2.5 + x = 2.738612788 Solving 2.5 + x = 2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.738612788 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.738612788 + -2.5 x = 2.738612788 + -2.5 Combine like terms: 2.738612788 + -2.5 = 0.238612788 x = 0.238612788 Simplifying x = 0.238612788Subproblem 2
x + 2.5 = -2.738612788 Simplifying x + 2.5 = -2.738612788 Reorder the terms: 2.5 + x = -2.738612788 Solving 2.5 + x = -2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.738612788 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.738612788 + -2.5 x = -2.738612788 + -2.5 Combine like terms: -2.738612788 + -2.5 = -5.238612788 x = -5.238612788 Simplifying x = -5.238612788Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.238612788, -5.238612788}Solution
x = {0.238612788, -5.238612788}
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