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Simplifying 4x2 + -20x + -125 = 0 Reorder the terms: -125 + -20x + 4x2 = 0 Solving -125 + -20x + 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 + -5x + x2 = 0 Move the constant term to the right: Add '31.25' to each side of the equation. -31.25 + -5x + 31.25 + x2 = 0 + 31.25 Reorder the terms: -31.25 + 31.25 + -5x + x2 = 0 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + -5x + x2 = 0 + 31.25 -5x + x2 = 0 + 31.25 Combine like terms: 0 + 31.25 = 31.25 -5x + x2 = 31.25 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 = 31.25 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 31.25 + 6.25 Combine like terms: 31.25 + 6.25 = 37.5 6.25 + -5x + x2 = 37.5 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 37.5 Calculate the square root of the right side: 6.123724357 Break this problem into two subproblems by setting (x + -2.5) equal to 6.123724357 and -6.123724357.Subproblem 1
x + -2.5 = 6.123724357 Simplifying x + -2.5 = 6.123724357 Reorder the terms: -2.5 + x = 6.123724357 Solving -2.5 + x = 6.123724357 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 = 6.123724357 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 6.123724357 + 2.5 x = 6.123724357 + 2.5 Combine like terms: 6.123724357 + 2.5 = 8.623724357 x = 8.623724357 Simplifying x = 8.623724357Subproblem 2
x + -2.5 = -6.123724357 Simplifying x + -2.5 = -6.123724357 Reorder the terms: -2.5 + x = -6.123724357 Solving -2.5 + x = -6.123724357 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 = -6.123724357 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -6.123724357 + 2.5 x = -6.123724357 + 2.5 Combine like terms: -6.123724357 + 2.5 = -3.623724357 x = -3.623724357 Simplifying x = -3.623724357Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.623724357, -3.623724357}
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