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Simplifying 4x2 + -25x + 5 = 0 Reorder the terms: 5 + -25x + 4x2 = 0 Solving 5 + -25x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -6.25x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -6.25x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -6.25x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -6.25x + x2 = 0 + -1.25 -6.25x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -6.25x + x2 = -1.25 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = -1.25 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = -1.25 + 9.765625 Combine like terms: -1.25 + 9.765625 = 8.515625 9.765625 + -6.25x + x2 = 8.515625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 8.515625 Calculate the square root of the right side: 2.918154382 Break this problem into two subproblems by setting (x + -3.125) equal to 2.918154382 and -2.918154382.Subproblem 1
x + -3.125 = 2.918154382 Simplifying x + -3.125 = 2.918154382 Reorder the terms: -3.125 + x = 2.918154382 Solving -3.125 + x = 2.918154382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 2.918154382 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 2.918154382 + 3.125 x = 2.918154382 + 3.125 Combine like terms: 2.918154382 + 3.125 = 6.043154382 x = 6.043154382 Simplifying x = 6.043154382Subproblem 2
x + -3.125 = -2.918154382 Simplifying x + -3.125 = -2.918154382 Reorder the terms: -3.125 + x = -2.918154382 Solving -3.125 + x = -2.918154382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -2.918154382 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -2.918154382 + 3.125 x = -2.918154382 + 3.125 Combine like terms: -2.918154382 + 3.125 = 0.206845618 x = 0.206845618 Simplifying x = 0.206845618Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.043154382, 0.206845618}
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