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Simplifying 0.2x2 + -9x + -1000 = 0 Reorder the terms: -1000 + -9x + 0.2x2 = 0 Solving -1000 + -9x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -5000 + -45x + x2 = 0 Move the constant term to the right: Add '5000' to each side of the equation. -5000 + -45x + 5000 + x2 = 0 + 5000 Reorder the terms: -5000 + 5000 + -45x + x2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + -45x + x2 = 0 + 5000 -45x + x2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 -45x + x2 = 5000 The x term is -45x. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45x + 506.25 + x2 = 5000 + 506.25 Reorder the terms: 506.25 + -45x + x2 = 5000 + 506.25 Combine like terms: 5000 + 506.25 = 5506.25 506.25 + -45x + x2 = 5506.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 5506.25 Calculate the square root of the right side: 74.204110398 Break this problem into two subproblems by setting (x + -22.5) equal to 74.204110398 and -74.204110398.Subproblem 1
x + -22.5 = 74.204110398 Simplifying x + -22.5 = 74.204110398 Reorder the terms: -22.5 + x = 74.204110398 Solving -22.5 + x = 74.204110398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = 74.204110398 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 74.204110398 + 22.5 x = 74.204110398 + 22.5 Combine like terms: 74.204110398 + 22.5 = 96.704110398 x = 96.704110398 Simplifying x = 96.704110398Subproblem 2
x + -22.5 = -74.204110398 Simplifying x + -22.5 = -74.204110398 Reorder the terms: -22.5 + x = -74.204110398 Solving -22.5 + x = -74.204110398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = -74.204110398 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -74.204110398 + 22.5 x = -74.204110398 + 22.5 Combine like terms: -74.204110398 + 22.5 = -51.704110398 x = -51.704110398 Simplifying x = -51.704110398Solution
The solution to the problem is based on the solutions from the subproblems. x = {96.704110398, -51.704110398}
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