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Simplifying 6750 + -465x + -1x2 = 0 Solving 6750 + -465x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6750 + 465x + x2 = 0 Move the constant term to the right: Add '6750' to each side of the equation. -6750 + 465x + 6750 + x2 = 0 + 6750 Reorder the terms: -6750 + 6750 + 465x + x2 = 0 + 6750 Combine like terms: -6750 + 6750 = 0 0 + 465x + x2 = 0 + 6750 465x + x2 = 0 + 6750 Combine like terms: 0 + 6750 = 6750 465x + x2 = 6750 The x term is 465x. Take half its coefficient (232.5). Square it (54056.25) and add it to both sides. Add '54056.25' to each side of the equation. 465x + 54056.25 + x2 = 6750 + 54056.25 Reorder the terms: 54056.25 + 465x + x2 = 6750 + 54056.25 Combine like terms: 6750 + 54056.25 = 60806.25 54056.25 + 465x + x2 = 60806.25 Factor a perfect square on the left side: (x + 232.5)(x + 232.5) = 60806.25 Calculate the square root of the right side: 246.589233342 Break this problem into two subproblems by setting (x + 232.5) equal to 246.589233342 and -246.589233342.Subproblem 1
x + 232.5 = 246.589233342 Simplifying x + 232.5 = 246.589233342 Reorder the terms: 232.5 + x = 246.589233342 Solving 232.5 + x = 246.589233342 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-232.5' to each side of the equation. 232.5 + -232.5 + x = 246.589233342 + -232.5 Combine like terms: 232.5 + -232.5 = 0.0 0.0 + x = 246.589233342 + -232.5 x = 246.589233342 + -232.5 Combine like terms: 246.589233342 + -232.5 = 14.089233342 x = 14.089233342 Simplifying x = 14.089233342Subproblem 2
x + 232.5 = -246.589233342 Simplifying x + 232.5 = -246.589233342 Reorder the terms: 232.5 + x = -246.589233342 Solving 232.5 + x = -246.589233342 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-232.5' to each side of the equation. 232.5 + -232.5 + x = -246.589233342 + -232.5 Combine like terms: 232.5 + -232.5 = 0.0 0.0 + x = -246.589233342 + -232.5 x = -246.589233342 + -232.5 Combine like terms: -246.589233342 + -232.5 = -479.089233342 x = -479.089233342 Simplifying x = -479.089233342Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.089233342, -479.089233342}
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