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Simplifying 4x2 + -1x + -125 = 0 Reorder the terms: -125 + -1x + 4x2 = 0 Solving -125 + -1x + 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'. -31.25 + -0.25x + x2 = 0 Move the constant term to the right: Add '31.25' to each side of the equation. -31.25 + -0.25x + 31.25 + x2 = 0 + 31.25 Reorder the terms: -31.25 + 31.25 + -0.25x + x2 = 0 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + -0.25x + x2 = 0 + 31.25 -0.25x + x2 = 0 + 31.25 Combine like terms: 0 + 31.25 = 31.25 -0.25x + x2 = 31.25 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 31.25 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 31.25 + 0.015625 Combine like terms: 31.25 + 0.015625 = 31.265625 0.015625 + -0.25x + x2 = 31.265625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 31.265625 Calculate the square root of the right side: 5.591567312 Break this problem into two subproblems by setting (x + -0.125) equal to 5.591567312 and -5.591567312.Subproblem 1
x + -0.125 = 5.591567312 Simplifying x + -0.125 = 5.591567312 Reorder the terms: -0.125 + x = 5.591567312 Solving -0.125 + x = 5.591567312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 5.591567312 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 5.591567312 + 0.125 x = 5.591567312 + 0.125 Combine like terms: 5.591567312 + 0.125 = 5.716567312 x = 5.716567312 Simplifying x = 5.716567312Subproblem 2
x + -0.125 = -5.591567312 Simplifying x + -0.125 = -5.591567312 Reorder the terms: -0.125 + x = -5.591567312 Solving -0.125 + x = -5.591567312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -5.591567312 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -5.591567312 + 0.125 x = -5.591567312 + 0.125 Combine like terms: -5.591567312 + 0.125 = -5.466567312 x = -5.466567312 Simplifying x = -5.466567312Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.716567312, -5.466567312}
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