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Simplifying -4x2 + 40x + 2 = 0 Reorder the terms: 2 + 40x + -4x2 = 0 Solving 2 + 40x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 20x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 20x + -2x2)' equal to zero and attempt to solve: Simplifying 1 + 20x + -2x2 = 0 Solving 1 + 20x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -10x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -10x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -10x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -10x + x2 = 0 + 0.5 -10x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -10x + x2 = 0.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 0.5 + 25 Reorder the terms: 25 + -10x + x2 = 0.5 + 25 Combine like terms: 0.5 + 25 = 25.5 25 + -10x + x2 = 25.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 25.5 Calculate the square root of the right side: 5.049752469 Break this problem into two subproblems by setting (x + -5) equal to 5.049752469 and -5.049752469.Subproblem 1
x + -5 = 5.049752469 Simplifying x + -5 = 5.049752469 Reorder the terms: -5 + x = 5.049752469 Solving -5 + x = 5.049752469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.049752469 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.049752469 + 5 x = 5.049752469 + 5 Combine like terms: 5.049752469 + 5 = 10.049752469 x = 10.049752469 Simplifying x = 10.049752469Subproblem 2
x + -5 = -5.049752469 Simplifying x + -5 = -5.049752469 Reorder the terms: -5 + x = -5.049752469 Solving -5 + x = -5.049752469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.049752469 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.049752469 + 5 x = -5.049752469 + 5 Combine like terms: -5.049752469 + 5 = -0.049752469 x = -0.049752469 Simplifying x = -0.049752469Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.049752469, -0.049752469}Solution
x = {10.049752469, -0.049752469}
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