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Simplifying 7x2 + -25x + -200 = 0 Reorder the terms: -200 + -25x + 7x2 = 0 Solving -200 + -25x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -28.57142857 + -3.571428571x + x2 = 0 Move the constant term to the right: Add '28.57142857' to each side of the equation. -28.57142857 + -3.571428571x + 28.57142857 + x2 = 0 + 28.57142857 Reorder the terms: -28.57142857 + 28.57142857 + -3.571428571x + x2 = 0 + 28.57142857 Combine like terms: -28.57142857 + 28.57142857 = 0.00000000 0.00000000 + -3.571428571x + x2 = 0 + 28.57142857 -3.571428571x + x2 = 0 + 28.57142857 Combine like terms: 0 + 28.57142857 = 28.57142857 -3.571428571x + x2 = 28.57142857 The x term is -3.571428571x. Take half its coefficient (-1.785714286). Square it (3.188775511) and add it to both sides. Add '3.188775511' to each side of the equation. -3.571428571x + 3.188775511 + x2 = 28.57142857 + 3.188775511 Reorder the terms: 3.188775511 + -3.571428571x + x2 = 28.57142857 + 3.188775511 Combine like terms: 28.57142857 + 3.188775511 = 31.760204081 3.188775511 + -3.571428571x + x2 = 31.760204081 Factor a perfect square on the left side: (x + -1.785714286)(x + -1.785714286) = 31.760204081 Calculate the square root of the right side: 5.635619228 Break this problem into two subproblems by setting (x + -1.785714286) equal to 5.635619228 and -5.635619228.Subproblem 1
x + -1.785714286 = 5.635619228 Simplifying x + -1.785714286 = 5.635619228 Reorder the terms: -1.785714286 + x = 5.635619228 Solving -1.785714286 + x = 5.635619228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = 5.635619228 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = 5.635619228 + 1.785714286 x = 5.635619228 + 1.785714286 Combine like terms: 5.635619228 + 1.785714286 = 7.421333514 x = 7.421333514 Simplifying x = 7.421333514Subproblem 2
x + -1.785714286 = -5.635619228 Simplifying x + -1.785714286 = -5.635619228 Reorder the terms: -1.785714286 + x = -5.635619228 Solving -1.785714286 + x = -5.635619228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = -5.635619228 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = -5.635619228 + 1.785714286 x = -5.635619228 + 1.785714286 Combine like terms: -5.635619228 + 1.785714286 = -3.849904942 x = -3.849904942 Simplifying x = -3.849904942Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.421333514, -3.849904942}
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