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Simplifying 9x2 + -26x + -5 = 0 Reorder the terms: -5 + -26x + 9x2 = 0 Solving -5 + -26x + 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'. -0.5555555556 + -2.888888889x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -2.888888889x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -2.888888889x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -2.888888889x + x2 = 0 + 0.5555555556 -2.888888889x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -2.888888889x + x2 = 0.5555555556 The x term is -2.888888889x. Take half its coefficient (-1.444444445). Square it (2.086419755) and add it to both sides. Add '2.086419755' to each side of the equation. -2.888888889x + 2.086419755 + x2 = 0.5555555556 + 2.086419755 Reorder the terms: 2.086419755 + -2.888888889x + x2 = 0.5555555556 + 2.086419755 Combine like terms: 0.5555555556 + 2.086419755 = 2.6419753106 2.086419755 + -2.888888889x + x2 = 2.6419753106 Factor a perfect square on the left side: (x + -1.444444445)(x + -1.444444445) = 2.6419753106 Calculate the square root of the right side: 1.625415427 Break this problem into two subproblems by setting (x + -1.444444445) equal to 1.625415427 and -1.625415427.Subproblem 1
x + -1.444444445 = 1.625415427 Simplifying x + -1.444444445 = 1.625415427 Reorder the terms: -1.444444445 + x = 1.625415427 Solving -1.444444445 + x = 1.625415427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.444444445' to each side of the equation. -1.444444445 + 1.444444445 + x = 1.625415427 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + x = 1.625415427 + 1.444444445 x = 1.625415427 + 1.444444445 Combine like terms: 1.625415427 + 1.444444445 = 3.069859872 x = 3.069859872 Simplifying x = 3.069859872Subproblem 2
x + -1.444444445 = -1.625415427 Simplifying x + -1.444444445 = -1.625415427 Reorder the terms: -1.444444445 + x = -1.625415427 Solving -1.444444445 + x = -1.625415427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.444444445' to each side of the equation. -1.444444445 + 1.444444445 + x = -1.625415427 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + x = -1.625415427 + 1.444444445 x = -1.625415427 + 1.444444445 Combine like terms: -1.625415427 + 1.444444445 = -0.180970982 x = -0.180970982 Simplifying x = -0.180970982Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.069859872, -0.180970982}
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