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Simplifying 210x2 + -1680 + 7700x = 6 Reorder the terms: -1680 + 7700x + 210x2 = 6 Solving -1680 + 7700x + 210x2 = 6 Solving for variable 'x'. Reorder the terms: -1680 + -6 + 7700x + 210x2 = 6 + -6 Combine like terms: -1680 + -6 = -1686 -1686 + 7700x + 210x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -1686 + 7700x + 210x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-843 + 3850x + 105x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-843 + 3850x + 105x2)' equal to zero and attempt to solve: Simplifying -843 + 3850x + 105x2 = 0 Solving -843 + 3850x + 105x2 = 0 Begin completing the square. Divide all terms by 105 the coefficient of the squared term: Divide each side by '105'. -8.028571429 + 36.66666667x + x2 = 0 Move the constant term to the right: Add '8.028571429' to each side of the equation. -8.028571429 + 36.66666667x + 8.028571429 + x2 = 0 + 8.028571429 Reorder the terms: -8.028571429 + 8.028571429 + 36.66666667x + x2 = 0 + 8.028571429 Combine like terms: -8.028571429 + 8.028571429 = 0.000000000 0.000000000 + 36.66666667x + x2 = 0 + 8.028571429 36.66666667x + x2 = 0 + 8.028571429 Combine like terms: 0 + 8.028571429 = 8.028571429 36.66666667x + x2 = 8.028571429 The x term is 36.66666667x. Take half its coefficient (18.33333334). Square it (336.1111114) and add it to both sides. Add '336.1111114' to each side of the equation. 36.66666667x + 336.1111114 + x2 = 8.028571429 + 336.1111114 Reorder the terms: 336.1111114 + 36.66666667x + x2 = 8.028571429 + 336.1111114 Combine like terms: 8.028571429 + 336.1111114 = 344.139682829 336.1111114 + 36.66666667x + x2 = 344.139682829 Factor a perfect square on the left side: (x + 18.33333334)(x + 18.33333334) = 344.139682829 Calculate the square root of the right side: 18.551002206 Break this problem into two subproblems by setting (x + 18.33333334) equal to 18.551002206 and -18.551002206.Subproblem 1
x + 18.33333334 = 18.551002206 Simplifying x + 18.33333334 = 18.551002206 Reorder the terms: 18.33333334 + x = 18.551002206 Solving 18.33333334 + x = 18.551002206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.33333334' to each side of the equation. 18.33333334 + -18.33333334 + x = 18.551002206 + -18.33333334 Combine like terms: 18.33333334 + -18.33333334 = 0.00000000 0.00000000 + x = 18.551002206 + -18.33333334 x = 18.551002206 + -18.33333334 Combine like terms: 18.551002206 + -18.33333334 = 0.217668866 x = 0.217668866 Simplifying x = 0.217668866Subproblem 2
x + 18.33333334 = -18.551002206 Simplifying x + 18.33333334 = -18.551002206 Reorder the terms: 18.33333334 + x = -18.551002206 Solving 18.33333334 + x = -18.551002206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.33333334' to each side of the equation. 18.33333334 + -18.33333334 + x = -18.551002206 + -18.33333334 Combine like terms: 18.33333334 + -18.33333334 = 0.00000000 0.00000000 + x = -18.551002206 + -18.33333334 x = -18.551002206 + -18.33333334 Combine like terms: -18.551002206 + -18.33333334 = -36.884335546 x = -36.884335546 Simplifying x = -36.884335546Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.217668866, -36.884335546}Solution
x = {0.217668866, -36.884335546}
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