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Simplifying 9x2 + -26x + -16 = 0 Reorder the terms: -16 + -26x + 9x2 = 0 Solving -16 + -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'. -1.777777778 + -2.888888889x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -2.888888889x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -2.888888889x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -2.888888889x + x2 = 0 + 1.777777778 -2.888888889x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -2.888888889x + x2 = 1.777777778 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 = 1.777777778 + 2.086419755 Reorder the terms: 2.086419755 + -2.888888889x + x2 = 1.777777778 + 2.086419755 Combine like terms: 1.777777778 + 2.086419755 = 3.864197533 2.086419755 + -2.888888889x + x2 = 3.864197533 Factor a perfect square on the left side: (x + -1.444444445)(x + -1.444444445) = 3.864197533 Calculate the square root of the right side: 1.965756224 Break this problem into two subproblems by setting (x + -1.444444445) equal to 1.965756224 and -1.965756224.Subproblem 1
x + -1.444444445 = 1.965756224 Simplifying x + -1.444444445 = 1.965756224 Reorder the terms: -1.444444445 + x = 1.965756224 Solving -1.444444445 + x = 1.965756224 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 = 1.965756224 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + x = 1.965756224 + 1.444444445 x = 1.965756224 + 1.444444445 Combine like terms: 1.965756224 + 1.444444445 = 3.410200669 x = 3.410200669 Simplifying x = 3.410200669Subproblem 2
x + -1.444444445 = -1.965756224 Simplifying x + -1.444444445 = -1.965756224 Reorder the terms: -1.444444445 + x = -1.965756224 Solving -1.444444445 + x = -1.965756224 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 = -1.965756224 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + x = -1.965756224 + 1.444444445 x = -1.965756224 + 1.444444445 Combine like terms: -1.965756224 + 1.444444445 = -0.521311779 x = -0.521311779 Simplifying x = -0.521311779Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.410200669, -0.521311779}
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