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Simplifying 3x2 + -78x + 200 = 0 Reorder the terms: 200 + -78x + 3x2 = 0 Solving 200 + -78x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 66.66666667 + -26x + x2 = 0 Move the constant term to the right: Add '-66.66666667' to each side of the equation. 66.66666667 + -26x + -66.66666667 + x2 = 0 + -66.66666667 Reorder the terms: 66.66666667 + -66.66666667 + -26x + x2 = 0 + -66.66666667 Combine like terms: 66.66666667 + -66.66666667 = 0.00000000 0.00000000 + -26x + x2 = 0 + -66.66666667 -26x + x2 = 0 + -66.66666667 Combine like terms: 0 + -66.66666667 = -66.66666667 -26x + x2 = -66.66666667 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -66.66666667 + 169 Reorder the terms: 169 + -26x + x2 = -66.66666667 + 169 Combine like terms: -66.66666667 + 169 = 102.33333333 169 + -26x + x2 = 102.33333333 Factor a perfect square on the left side: (x + -13)(x + -13) = 102.33333333 Calculate the square root of the right side: 10.115993937 Break this problem into two subproblems by setting (x + -13) equal to 10.115993937 and -10.115993937.Subproblem 1
x + -13 = 10.115993937 Simplifying x + -13 = 10.115993937 Reorder the terms: -13 + x = 10.115993937 Solving -13 + x = 10.115993937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 10.115993937 + 13 Combine like terms: -13 + 13 = 0 0 + x = 10.115993937 + 13 x = 10.115993937 + 13 Combine like terms: 10.115993937 + 13 = 23.115993937 x = 23.115993937 Simplifying x = 23.115993937Subproblem 2
x + -13 = -10.115993937 Simplifying x + -13 = -10.115993937 Reorder the terms: -13 + x = -10.115993937 Solving -13 + x = -10.115993937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -10.115993937 + 13 Combine like terms: -13 + 13 = 0 0 + x = -10.115993937 + 13 x = -10.115993937 + 13 Combine like terms: -10.115993937 + 13 = 2.884006063 x = 2.884006063 Simplifying x = 2.884006063Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.115993937, 2.884006063}
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