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Simplifying -1x2 + -100x + 717 = 0 Reorder the terms: 717 + -100x + -1x2 = 0 Solving 717 + -100x + -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'. -717 + 100x + x2 = 0 Move the constant term to the right: Add '717' to each side of the equation. -717 + 100x + 717 + x2 = 0 + 717 Reorder the terms: -717 + 717 + 100x + x2 = 0 + 717 Combine like terms: -717 + 717 = 0 0 + 100x + x2 = 0 + 717 100x + x2 = 0 + 717 Combine like terms: 0 + 717 = 717 100x + x2 = 717 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = 717 + 2500 Reorder the terms: 2500 + 100x + x2 = 717 + 2500 Combine like terms: 717 + 2500 = 3217 2500 + 100x + x2 = 3217 Factor a perfect square on the left side: (x + 50)(x + 50) = 3217 Calculate the square root of the right side: 56.71860365 Break this problem into two subproblems by setting (x + 50) equal to 56.71860365 and -56.71860365.Subproblem 1
x + 50 = 56.71860365 Simplifying x + 50 = 56.71860365 Reorder the terms: 50 + x = 56.71860365 Solving 50 + x = 56.71860365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 56.71860365 + -50 Combine like terms: 50 + -50 = 0 0 + x = 56.71860365 + -50 x = 56.71860365 + -50 Combine like terms: 56.71860365 + -50 = 6.71860365 x = 6.71860365 Simplifying x = 6.71860365Subproblem 2
x + 50 = -56.71860365 Simplifying x + 50 = -56.71860365 Reorder the terms: 50 + x = -56.71860365 Solving 50 + x = -56.71860365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -56.71860365 + -50 Combine like terms: 50 + -50 = 0 0 + x = -56.71860365 + -50 x = -56.71860365 + -50 Combine like terms: -56.71860365 + -50 = -106.71860365 x = -106.71860365 Simplifying x = -106.71860365Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.71860365, -106.71860365}
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