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Simplifying 0 = x2 + 35x + -1000 Reorder the terms: 0 = -1000 + 35x + x2 Solving 0 = -1000 + 35x + x2 Solving for variable 'x'. Combine like terms: 0 + 1000 = 1000 1000 + -35x + -1x2 = -1000 + 35x + x2 + 1000 + -35x + -1x2 Reorder the terms: 1000 + -35x + -1x2 = -1000 + 1000 + 35x + -35x + x2 + -1x2 Combine like terms: -1000 + 1000 = 0 1000 + -35x + -1x2 = 0 + 35x + -35x + x2 + -1x2 1000 + -35x + -1x2 = 35x + -35x + x2 + -1x2 Combine like terms: 35x + -35x = 0 1000 + -35x + -1x2 = 0 + x2 + -1x2 1000 + -35x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1000 + -35x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1000 + 35x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 35x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 35x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 35x + x2 = 0 + 1000 35x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 35x + x2 = 1000 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = 1000 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 1000 + 306.25 Combine like terms: 1000 + 306.25 = 1306.25 306.25 + 35x + x2 = 1306.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 1306.25 Calculate the square root of the right side: 36.142080737 Break this problem into two subproblems by setting (x + 17.5) equal to 36.142080737 and -36.142080737.Subproblem 1
x + 17.5 = 36.142080737 Simplifying x + 17.5 = 36.142080737 Reorder the terms: 17.5 + x = 36.142080737 Solving 17.5 + x = 36.142080737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 36.142080737 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 36.142080737 + -17.5 x = 36.142080737 + -17.5 Combine like terms: 36.142080737 + -17.5 = 18.642080737 x = 18.642080737 Simplifying x = 18.642080737Subproblem 2
x + 17.5 = -36.142080737 Simplifying x + 17.5 = -36.142080737 Reorder the terms: 17.5 + x = -36.142080737 Solving 17.5 + x = -36.142080737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -36.142080737 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -36.142080737 + -17.5 x = -36.142080737 + -17.5 Combine like terms: -36.142080737 + -17.5 = -53.642080737 x = -53.642080737 Simplifying x = -53.642080737Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.642080737, -53.642080737}
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