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Simplifying 4x2 + -23x + -500 = 0 Reorder the terms: -500 + -23x + 4x2 = 0 Solving -500 + -23x + 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'. -125 + -5.75x + x2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + -5.75x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + -5.75x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -5.75x + x2 = 0 + 125 -5.75x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 -5.75x + x2 = 125 The x term is -5.75x. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75x + 8.265625 + x2 = 125 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = 125 + 8.265625 Combine like terms: 125 + 8.265625 = 133.265625 8.265625 + -5.75x + x2 = 133.265625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 133.265625 Calculate the square root of the right side: 11.544073155 Break this problem into two subproblems by setting (x + -2.875) equal to 11.544073155 and -11.544073155.Subproblem 1
x + -2.875 = 11.544073155 Simplifying x + -2.875 = 11.544073155 Reorder the terms: -2.875 + x = 11.544073155 Solving -2.875 + x = 11.544073155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 11.544073155 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 11.544073155 + 2.875 x = 11.544073155 + 2.875 Combine like terms: 11.544073155 + 2.875 = 14.419073155 x = 14.419073155 Simplifying x = 14.419073155Subproblem 2
x + -2.875 = -11.544073155 Simplifying x + -2.875 = -11.544073155 Reorder the terms: -2.875 + x = -11.544073155 Solving -2.875 + x = -11.544073155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -11.544073155 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -11.544073155 + 2.875 x = -11.544073155 + 2.875 Combine like terms: -11.544073155 + 2.875 = -8.669073155 x = -8.669073155 Simplifying x = -8.669073155Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.419073155, -8.669073155}
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