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Simplifying 9x2 + 26x + 16 = 36 Reorder the terms: 16 + 26x + 9x2 = 36 Solving 16 + 26x + 9x2 = 36 Solving for variable 'x'. Reorder the terms: 16 + -36 + 26x + 9x2 = 36 + -36 Combine like terms: 16 + -36 = -20 -20 + 26x + 9x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -20 + 26x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + 2.888888889x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + 2.888888889x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + 2.888888889x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + 2.888888889x + x2 = 0 + 2.222222222 2.888888889x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 2.888888889x + x2 = 2.222222222 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 = 2.222222222 + 2.086419755 Reorder the terms: 2.086419755 + 2.888888889x + x2 = 2.222222222 + 2.086419755 Combine like terms: 2.222222222 + 2.086419755 = 4.308641977 2.086419755 + 2.888888889x + x2 = 4.308641977 Factor a perfect square on the left side: (x + 1.444444445)(x + 1.444444445) = 4.308641977 Calculate the square root of the right side: 2.075726855 Break this problem into two subproblems by setting (x + 1.444444445) equal to 2.075726855 and -2.075726855.Subproblem 1
x + 1.444444445 = 2.075726855 Simplifying x + 1.444444445 = 2.075726855 Reorder the terms: 1.444444445 + x = 2.075726855 Solving 1.444444445 + x = 2.075726855 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 = 2.075726855 + -1.444444445 Combine like terms: 1.444444445 + -1.444444445 = 0.000000000 0.000000000 + x = 2.075726855 + -1.444444445 x = 2.075726855 + -1.444444445 Combine like terms: 2.075726855 + -1.444444445 = 0.63128241 x = 0.63128241 Simplifying x = 0.63128241Subproblem 2
x + 1.444444445 = -2.075726855 Simplifying x + 1.444444445 = -2.075726855 Reorder the terms: 1.444444445 + x = -2.075726855 Solving 1.444444445 + x = -2.075726855 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 = -2.075726855 + -1.444444445 Combine like terms: 1.444444445 + -1.444444445 = 0.000000000 0.000000000 + x = -2.075726855 + -1.444444445 x = -2.075726855 + -1.444444445 Combine like terms: -2.075726855 + -1.444444445 = -3.5201713 x = -3.5201713 Simplifying x = -3.5201713Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.63128241, -3.5201713}
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