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Simplifying -1x2 + 980x + -3000 = 0 Reorder the terms: -3000 + 980x + -1x2 = 0 Solving -3000 + 980x + -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'. 3000 + -980x + x2 = 0 Move the constant term to the right: Add '-3000' to each side of the equation. 3000 + -980x + -3000 + x2 = 0 + -3000 Reorder the terms: 3000 + -3000 + -980x + x2 = 0 + -3000 Combine like terms: 3000 + -3000 = 0 0 + -980x + x2 = 0 + -3000 -980x + x2 = 0 + -3000 Combine like terms: 0 + -3000 = -3000 -980x + x2 = -3000 The x term is -980x. Take half its coefficient (-490). Square it (240100) and add it to both sides. Add '240100' to each side of the equation. -980x + 240100 + x2 = -3000 + 240100 Reorder the terms: 240100 + -980x + x2 = -3000 + 240100 Combine like terms: -3000 + 240100 = 237100 240100 + -980x + x2 = 237100 Factor a perfect square on the left side: (x + -490)(x + -490) = 237100 Calculate the square root of the right side: 486.929152958 Break this problem into two subproblems by setting (x + -490) equal to 486.929152958 and -486.929152958.Subproblem 1
x + -490 = 486.929152958 Simplifying x + -490 = 486.929152958 Reorder the terms: -490 + x = 486.929152958 Solving -490 + x = 486.929152958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '490' to each side of the equation. -490 + 490 + x = 486.929152958 + 490 Combine like terms: -490 + 490 = 0 0 + x = 486.929152958 + 490 x = 486.929152958 + 490 Combine like terms: 486.929152958 + 490 = 976.929152958 x = 976.929152958 Simplifying x = 976.929152958Subproblem 2
x + -490 = -486.929152958 Simplifying x + -490 = -486.929152958 Reorder the terms: -490 + x = -486.929152958 Solving -490 + x = -486.929152958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '490' to each side of the equation. -490 + 490 + x = -486.929152958 + 490 Combine like terms: -490 + 490 = 0 0 + x = -486.929152958 + 490 x = -486.929152958 + 490 Combine like terms: -486.929152958 + 490 = 3.070847042 x = 3.070847042 Simplifying x = 3.070847042Solution
The solution to the problem is based on the solutions from the subproblems. x = {976.929152958, 3.070847042}
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