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Simplifying 9x2 + -107x + 276 = 0 Reorder the terms: 276 + -107x + 9x2 = 0 Solving 276 + -107x + 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'. 30.66666667 + -11.88888889x + x2 = 0 Move the constant term to the right: Add '-30.66666667' to each side of the equation. 30.66666667 + -11.88888889x + -30.66666667 + x2 = 0 + -30.66666667 Reorder the terms: 30.66666667 + -30.66666667 + -11.88888889x + x2 = 0 + -30.66666667 Combine like terms: 30.66666667 + -30.66666667 = 0.00000000 0.00000000 + -11.88888889x + x2 = 0 + -30.66666667 -11.88888889x + x2 = 0 + -30.66666667 Combine like terms: 0 + -30.66666667 = -30.66666667 -11.88888889x + x2 = -30.66666667 The x term is -11.88888889x. Take half its coefficient (-5.944444445). Square it (35.33641976) and add it to both sides. Add '35.33641976' to each side of the equation. -11.88888889x + 35.33641976 + x2 = -30.66666667 + 35.33641976 Reorder the terms: 35.33641976 + -11.88888889x + x2 = -30.66666667 + 35.33641976 Combine like terms: -30.66666667 + 35.33641976 = 4.66975309 35.33641976 + -11.88888889x + x2 = 4.66975309 Factor a perfect square on the left side: (x + -5.944444445)(x + -5.944444445) = 4.66975309 Calculate the square root of the right side: 2.16096115 Break this problem into two subproblems by setting (x + -5.944444445) equal to 2.16096115 and -2.16096115.Subproblem 1
x + -5.944444445 = 2.16096115 Simplifying x + -5.944444445 = 2.16096115 Reorder the terms: -5.944444445 + x = 2.16096115 Solving -5.944444445 + x = 2.16096115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.944444445' to each side of the equation. -5.944444445 + 5.944444445 + x = 2.16096115 + 5.944444445 Combine like terms: -5.944444445 + 5.944444445 = 0.000000000 0.000000000 + x = 2.16096115 + 5.944444445 x = 2.16096115 + 5.944444445 Combine like terms: 2.16096115 + 5.944444445 = 8.105405595 x = 8.105405595 Simplifying x = 8.105405595Subproblem 2
x + -5.944444445 = -2.16096115 Simplifying x + -5.944444445 = -2.16096115 Reorder the terms: -5.944444445 + x = -2.16096115 Solving -5.944444445 + x = -2.16096115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.944444445' to each side of the equation. -5.944444445 + 5.944444445 + x = -2.16096115 + 5.944444445 Combine like terms: -5.944444445 + 5.944444445 = 0.000000000 0.000000000 + x = -2.16096115 + 5.944444445 x = -2.16096115 + 5.944444445 Combine like terms: -2.16096115 + 5.944444445 = 3.783483295 x = 3.783483295 Simplifying x = 3.783483295Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.105405595, 3.783483295}
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