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Simplifying 9x2 + -44x + -156 = 0 Reorder the terms: -156 + -44x + 9x2 = 0 Solving -156 + -44x + 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'. -17.33333333 + -4.888888889x + x2 = 0 Move the constant term to the right: Add '17.33333333' to each side of the equation. -17.33333333 + -4.888888889x + 17.33333333 + x2 = 0 + 17.33333333 Reorder the terms: -17.33333333 + 17.33333333 + -4.888888889x + x2 = 0 + 17.33333333 Combine like terms: -17.33333333 + 17.33333333 = 0.00000000 0.00000000 + -4.888888889x + x2 = 0 + 17.33333333 -4.888888889x + x2 = 0 + 17.33333333 Combine like terms: 0 + 17.33333333 = 17.33333333 -4.888888889x + x2 = 17.33333333 The x term is -4.888888889x. Take half its coefficient (-2.444444445). Square it (5.975308645) and add it to both sides. Add '5.975308645' to each side of the equation. -4.888888889x + 5.975308645 + x2 = 17.33333333 + 5.975308645 Reorder the terms: 5.975308645 + -4.888888889x + x2 = 17.33333333 + 5.975308645 Combine like terms: 17.33333333 + 5.975308645 = 23.308641975 5.975308645 + -4.888888889x + x2 = 23.308641975 Factor a perfect square on the left side: (x + -2.444444445)(x + -2.444444445) = 23.308641975 Calculate the square root of the right side: 4.827902441 Break this problem into two subproblems by setting (x + -2.444444445) equal to 4.827902441 and -4.827902441.Subproblem 1
x + -2.444444445 = 4.827902441 Simplifying x + -2.444444445 = 4.827902441 Reorder the terms: -2.444444445 + x = 4.827902441 Solving -2.444444445 + x = 4.827902441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.444444445' to each side of the equation. -2.444444445 + 2.444444445 + x = 4.827902441 + 2.444444445 Combine like terms: -2.444444445 + 2.444444445 = 0.000000000 0.000000000 + x = 4.827902441 + 2.444444445 x = 4.827902441 + 2.444444445 Combine like terms: 4.827902441 + 2.444444445 = 7.272346886 x = 7.272346886 Simplifying x = 7.272346886Subproblem 2
x + -2.444444445 = -4.827902441 Simplifying x + -2.444444445 = -4.827902441 Reorder the terms: -2.444444445 + x = -4.827902441 Solving -2.444444445 + x = -4.827902441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.444444445' to each side of the equation. -2.444444445 + 2.444444445 + x = -4.827902441 + 2.444444445 Combine like terms: -2.444444445 + 2.444444445 = 0.000000000 0.000000000 + x = -4.827902441 + 2.444444445 x = -4.827902441 + 2.444444445 Combine like terms: -4.827902441 + 2.444444445 = -2.383457996 x = -2.383457996 Simplifying x = -2.383457996Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.272346886, -2.383457996}
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