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Simplifying 1.96x2 + -8x + -7000 = 0 Reorder the terms: -7000 + -8x + 1.96x2 = 0 Solving -7000 + -8x + 1.96x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.96 the coefficient of the squared term: Divide each side by '1.96'. -3571.428571 + -4.081632653x + x2 = 0 Move the constant term to the right: Add '3571.428571' to each side of the equation. -3571.428571 + -4.081632653x + 3571.428571 + x2 = 0 + 3571.428571 Reorder the terms: -3571.428571 + 3571.428571 + -4.081632653x + x2 = 0 + 3571.428571 Combine like terms: -3571.428571 + 3571.428571 = 0.000000 0.000000 + -4.081632653x + x2 = 0 + 3571.428571 -4.081632653x + x2 = 0 + 3571.428571 Combine like terms: 0 + 3571.428571 = 3571.428571 -4.081632653x + x2 = 3571.428571 The x term is -4.081632653x. Take half its coefficient (-2.040816327). Square it (4.164931281) and add it to both sides. Add '4.164931281' to each side of the equation. -4.081632653x + 4.164931281 + x2 = 3571.428571 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653x + x2 = 3571.428571 + 4.164931281 Combine like terms: 3571.428571 + 4.164931281 = 3575.593502281 4.164931281 + -4.081632653x + x2 = 3575.593502281 Factor a perfect square on the left side: (x + -2.040816327)(x + -2.040816327) = 3575.593502281 Calculate the square root of the right side: 59.796266625 Break this problem into two subproblems by setting (x + -2.040816327) equal to 59.796266625 and -59.796266625.Subproblem 1
x + -2.040816327 = 59.796266625 Simplifying x + -2.040816327 = 59.796266625 Reorder the terms: -2.040816327 + x = 59.796266625 Solving -2.040816327 + x = 59.796266625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + x = 59.796266625 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = 59.796266625 + 2.040816327 x = 59.796266625 + 2.040816327 Combine like terms: 59.796266625 + 2.040816327 = 61.837082952 x = 61.837082952 Simplifying x = 61.837082952Subproblem 2
x + -2.040816327 = -59.796266625 Simplifying x + -2.040816327 = -59.796266625 Reorder the terms: -2.040816327 + x = -59.796266625 Solving -2.040816327 + x = -59.796266625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + x = -59.796266625 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = -59.796266625 + 2.040816327 x = -59.796266625 + 2.040816327 Combine like terms: -59.796266625 + 2.040816327 = -57.755450298 x = -57.755450298 Simplifying x = -57.755450298Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.837082952, -57.755450298}
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