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Simplifying 9x2 + -376x + 3600 = 0 Reorder the terms: 3600 + -376x + 9x2 = 0 Solving 3600 + -376x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 400 + -41.77777778x + x2 = 0 Move the constant term to the right: Add '-400' to each side of the equation. 400 + -41.77777778x + -400 + x2 = 0 + -400 Reorder the terms: 400 + -400 + -41.77777778x + x2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -41.77777778x + x2 = 0 + -400 -41.77777778x + x2 = 0 + -400 Combine like terms: 0 + -400 = -400 -41.77777778x + x2 = -400 The x term is -41.77777778x. Take half its coefficient (-20.88888889). Square it (436.3456791) and add it to both sides. Add '436.3456791' to each side of the equation. -41.77777778x + 436.3456791 + x2 = -400 + 436.3456791 Reorder the terms: 436.3456791 + -41.77777778x + x2 = -400 + 436.3456791 Combine like terms: -400 + 436.3456791 = 36.3456791 436.3456791 + -41.77777778x + x2 = 36.3456791 Factor a perfect square on the left side: (x + -20.88888889)(x + -20.88888889) = 36.3456791 Calculate the square root of the right side: 6.02873777 Break this problem into two subproblems by setting (x + -20.88888889) equal to 6.02873777 and -6.02873777.Subproblem 1
x + -20.88888889 = 6.02873777 Simplifying x + -20.88888889 = 6.02873777 Reorder the terms: -20.88888889 + x = 6.02873777 Solving -20.88888889 + x = 6.02873777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.88888889' to each side of the equation. -20.88888889 + 20.88888889 + x = 6.02873777 + 20.88888889 Combine like terms: -20.88888889 + 20.88888889 = 0.00000000 0.00000000 + x = 6.02873777 + 20.88888889 x = 6.02873777 + 20.88888889 Combine like terms: 6.02873777 + 20.88888889 = 26.91762666 x = 26.91762666 Simplifying x = 26.91762666Subproblem 2
x + -20.88888889 = -6.02873777 Simplifying x + -20.88888889 = -6.02873777 Reorder the terms: -20.88888889 + x = -6.02873777 Solving -20.88888889 + x = -6.02873777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.88888889' to each side of the equation. -20.88888889 + 20.88888889 + x = -6.02873777 + 20.88888889 Combine like terms: -20.88888889 + 20.88888889 = 0.00000000 0.00000000 + x = -6.02873777 + 20.88888889 x = -6.02873777 + 20.88888889 Combine like terms: -6.02873777 + 20.88888889 = 14.86015112 x = 14.86015112 Simplifying x = 14.86015112Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.91762666, 14.86015112}
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