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Simplifying 4x2 + -25x + -4 = 0 Reorder the terms: -4 + -25x + 4x2 = 0 Solving -4 + -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 + -6.25x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -6.25x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -6.25x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6.25x + x2 = 0 + 1 -6.25x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6.25x + x2 = 1 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 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 1 + 9.765625 Combine like terms: 1 + 9.765625 = 10.765625 9.765625 + -6.25x + x2 = 10.765625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 10.765625 Calculate the square root of the right side: 3.281101187 Break this problem into two subproblems by setting (x + -3.125) equal to 3.281101187 and -3.281101187.Subproblem 1
x + -3.125 = 3.281101187 Simplifying x + -3.125 = 3.281101187 Reorder the terms: -3.125 + x = 3.281101187 Solving -3.125 + x = 3.281101187 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 = 3.281101187 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 3.281101187 + 3.125 x = 3.281101187 + 3.125 Combine like terms: 3.281101187 + 3.125 = 6.406101187 x = 6.406101187 Simplifying x = 6.406101187Subproblem 2
x + -3.125 = -3.281101187 Simplifying x + -3.125 = -3.281101187 Reorder the terms: -3.125 + x = -3.281101187 Solving -3.125 + x = -3.281101187 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 = -3.281101187 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -3.281101187 + 3.125 x = -3.281101187 + 3.125 Combine like terms: -3.281101187 + 3.125 = -0.156101187 x = -0.156101187 Simplifying x = -0.156101187Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.406101187, -0.156101187}
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