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Simplifying 209 = (-5x2 + 66x) Reorder the terms: 209 = (66x + -5x2) Remove parenthesis around (66x + -5x2) 209 = 66x + -5x2 Solving 209 = 66x + -5x2 Solving for variable 'x'. Reorder the terms: 209 + -66x + 5x2 = 66x + -66x + -5x2 + 5x2 Combine like terms: 66x + -66x = 0 209 + -66x + 5x2 = 0 + -5x2 + 5x2 209 + -66x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 209 + -66x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 41.8 + -13.2x + x2 = 0 Move the constant term to the right: Add '-41.8' to each side of the equation. 41.8 + -13.2x + -41.8 + x2 = 0 + -41.8 Reorder the terms: 41.8 + -41.8 + -13.2x + x2 = 0 + -41.8 Combine like terms: 41.8 + -41.8 = 0.0 0.0 + -13.2x + x2 = 0 + -41.8 -13.2x + x2 = 0 + -41.8 Combine like terms: 0 + -41.8 = -41.8 -13.2x + x2 = -41.8 The x term is -13.2x. Take half its coefficient (-6.6). Square it (43.56) and add it to both sides. Add '43.56' to each side of the equation. -13.2x + 43.56 + x2 = -41.8 + 43.56 Reorder the terms: 43.56 + -13.2x + x2 = -41.8 + 43.56 Combine like terms: -41.8 + 43.56 = 1.76 43.56 + -13.2x + x2 = 1.76 Factor a perfect square on the left side: (x + -6.6)(x + -6.6) = 1.76 Calculate the square root of the right side: 1.326649916 Break this problem into two subproblems by setting (x + -6.6) equal to 1.326649916 and -1.326649916.Subproblem 1
x + -6.6 = 1.326649916 Simplifying x + -6.6 = 1.326649916 Reorder the terms: -6.6 + x = 1.326649916 Solving -6.6 + x = 1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.6' to each side of the equation. -6.6 + 6.6 + x = 1.326649916 + 6.6 Combine like terms: -6.6 + 6.6 = 0.0 0.0 + x = 1.326649916 + 6.6 x = 1.326649916 + 6.6 Combine like terms: 1.326649916 + 6.6 = 7.926649916 x = 7.926649916 Simplifying x = 7.926649916Subproblem 2
x + -6.6 = -1.326649916 Simplifying x + -6.6 = -1.326649916 Reorder the terms: -6.6 + x = -1.326649916 Solving -6.6 + x = -1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.6' to each side of the equation. -6.6 + 6.6 + x = -1.326649916 + 6.6 Combine like terms: -6.6 + 6.6 = 0.0 0.0 + x = -1.326649916 + 6.6 x = -1.326649916 + 6.6 Combine like terms: -1.326649916 + 6.6 = 5.273350084 x = 5.273350084 Simplifying x = 5.273350084Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.926649916, 5.273350084}
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