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Simplifying 0 = 9x2 + 26x + -11 Reorder the terms: 0 = -11 + 26x + 9x2 Solving 0 = -11 + 26x + 9x2 Solving for variable 'x'. Combine like terms: 0 + 11 = 11 11 + -26x + -9x2 = -11 + 26x + 9x2 + 11 + -26x + -9x2 Reorder the terms: 11 + -26x + -9x2 = -11 + 11 + 26x + -26x + 9x2 + -9x2 Combine like terms: -11 + 11 = 0 11 + -26x + -9x2 = 0 + 26x + -26x + 9x2 + -9x2 11 + -26x + -9x2 = 26x + -26x + 9x2 + -9x2 Combine like terms: 26x + -26x = 0 11 + -26x + -9x2 = 0 + 9x2 + -9x2 11 + -26x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 11 + -26x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1.222222222 + 2.888888889x + x2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + 2.888888889x + 1.222222222 + x2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + 2.888888889x + x2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + 2.888888889x + x2 = 0 + 1.222222222 2.888888889x + x2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 2.888888889x + x2 = 1.222222222 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 = 1.222222222 + 2.086419755 Reorder the terms: 2.086419755 + 2.888888889x + x2 = 1.222222222 + 2.086419755 Combine like terms: 1.222222222 + 2.086419755 = 3.308641977 2.086419755 + 2.888888889x + x2 = 3.308641977 Factor a perfect square on the left side: (x + 1.444444445)(x + 1.444444445) = 3.308641977 Calculate the square root of the right side: 1.818967283 Break this problem into two subproblems by setting (x + 1.444444445) equal to 1.818967283 and -1.818967283.Subproblem 1
x + 1.444444445 = 1.818967283 Simplifying x + 1.444444445 = 1.818967283 Reorder the terms: 1.444444445 + x = 1.818967283 Solving 1.444444445 + x = 1.818967283 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 = 1.818967283 + -1.444444445 Combine like terms: 1.444444445 + -1.444444445 = 0.000000000 0.000000000 + x = 1.818967283 + -1.444444445 x = 1.818967283 + -1.444444445 Combine like terms: 1.818967283 + -1.444444445 = 0.374522838 x = 0.374522838 Simplifying x = 0.374522838Subproblem 2
x + 1.444444445 = -1.818967283 Simplifying x + 1.444444445 = -1.818967283 Reorder the terms: 1.444444445 + x = -1.818967283 Solving 1.444444445 + x = -1.818967283 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 = -1.818967283 + -1.444444445 Combine like terms: 1.444444445 + -1.444444445 = 0.000000000 0.000000000 + x = -1.818967283 + -1.444444445 x = -1.818967283 + -1.444444445 Combine like terms: -1.818967283 + -1.444444445 = -3.263411728 x = -3.263411728 Simplifying x = -3.263411728Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.374522838, -3.263411728}
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