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Simplifying 0 = 3900x + 217 + -23.49x2 Reorder the terms: 0 = 217 + 3900x + -23.49x2 Solving 0 = 217 + 3900x + -23.49x2 Solving for variable 'x'. Combine like terms: 0 + -217 = -217 -217 + -3900x + 23.49x2 = 217 + 3900x + -23.49x2 + -217 + -3900x + 23.49x2 Reorder the terms: -217 + -3900x + 23.49x2 = 217 + -217 + 3900x + -3900x + -23.49x2 + 23.49x2 Combine like terms: 217 + -217 = 0 -217 + -3900x + 23.49x2 = 0 + 3900x + -3900x + -23.49x2 + 23.49x2 -217 + -3900x + 23.49x2 = 3900x + -3900x + -23.49x2 + 23.49x2 Combine like terms: 3900x + -3900x = 0 -217 + -3900x + 23.49x2 = 0 + -23.49x2 + 23.49x2 -217 + -3900x + 23.49x2 = -23.49x2 + 23.49x2 Combine like terms: -23.49x2 + 23.49x2 = 0.00 -217 + -3900x + 23.49x2 = 0.00 Begin completing the square. Divide all terms by 23.49 the coefficient of the squared term: Divide each side by '23.49'. -9.237973606 + -166.0280971x + x2 = 0 Move the constant term to the right: Add '9.237973606' to each side of the equation. -9.237973606 + -166.0280971x + 9.237973606 + x2 = 0 + 9.237973606 Reorder the terms: -9.237973606 + 9.237973606 + -166.0280971x + x2 = 0 + 9.237973606 Combine like terms: -9.237973606 + 9.237973606 = 0.000000000 0.000000000 + -166.0280971x + x2 = 0 + 9.237973606 -166.0280971x + x2 = 0 + 9.237973606 Combine like terms: 0 + 9.237973606 = 9.237973606 -166.0280971x + x2 = 9.237973606 The x term is -166.0280971x. Take half its coefficient (-83.01404855). Square it (6891.332257) and add it to both sides. Add '6891.332257' to each side of the equation. -166.0280971x + 6891.332257 + x2 = 9.237973606 + 6891.332257 Reorder the terms: 6891.332257 + -166.0280971x + x2 = 9.237973606 + 6891.332257 Combine like terms: 9.237973606 + 6891.332257 = 6900.570230606 6891.332257 + -166.0280971x + x2 = 6900.570230606 Factor a perfect square on the left side: (x + -83.01404855)(x + -83.01404855) = 6900.570230606 Calculate the square root of the right side: 83.069670943 Break this problem into two subproblems by setting (x + -83.01404855) equal to 83.069670943 and -83.069670943.Subproblem 1
x + -83.01404855 = 83.069670943 Simplifying x + -83.01404855 = 83.069670943 Reorder the terms: -83.01404855 + x = 83.069670943 Solving -83.01404855 + x = 83.069670943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '83.01404855' to each side of the equation. -83.01404855 + 83.01404855 + x = 83.069670943 + 83.01404855 Combine like terms: -83.01404855 + 83.01404855 = 0.00000000 0.00000000 + x = 83.069670943 + 83.01404855 x = 83.069670943 + 83.01404855 Combine like terms: 83.069670943 + 83.01404855 = 166.083719493 x = 166.083719493 Simplifying x = 166.083719493Subproblem 2
x + -83.01404855 = -83.069670943 Simplifying x + -83.01404855 = -83.069670943 Reorder the terms: -83.01404855 + x = -83.069670943 Solving -83.01404855 + x = -83.069670943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '83.01404855' to each side of the equation. -83.01404855 + 83.01404855 + x = -83.069670943 + 83.01404855 Combine like terms: -83.01404855 + 83.01404855 = 0.00000000 0.00000000 + x = -83.069670943 + 83.01404855 x = -83.069670943 + 83.01404855 Combine like terms: -83.069670943 + 83.01404855 = -0.055622393 x = -0.055622393 Simplifying x = -0.055622393Solution
The solution to the problem is based on the solutions from the subproblems. x = {166.083719493, -0.055622393}
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