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Simplifying 9x2 + 26x + -18 = 0 Reorder the terms: -18 + 26x + 9x2 = 0 Solving -18 + 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'. -2 + 2.888888889x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2.888888889x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 2.888888889x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2.888888889x + x2 = 0 + 2 2.888888889x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 2.888888889x + x2 = 2 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 + 2.086419755 Reorder the terms: 2.086419755 + 2.888888889x + x2 = 2 + 2.086419755 Combine like terms: 2 + 2.086419755 = 4.086419755 2.086419755 + 2.888888889x + x2 = 4.086419755 Factor a perfect square on the left side: (x + 1.444444445)(x + 1.444444445) = 4.086419755 Calculate the square root of the right side: 2.021489489 Break this problem into two subproblems by setting (x + 1.444444445) equal to 2.021489489 and -2.021489489.Subproblem 1
x + 1.444444445 = 2.021489489 Simplifying x + 1.444444445 = 2.021489489 Reorder the terms: 1.444444445 + x = 2.021489489 Solving 1.444444445 + x = 2.021489489 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 = 2.021489489 + -1.444444445 Combine like terms: 1.444444445 + -1.444444445 = 0.000000000 0.000000000 + x = 2.021489489 + -1.444444445 x = 2.021489489 + -1.444444445 Combine like terms: 2.021489489 + -1.444444445 = 0.577045044 x = 0.577045044 Simplifying x = 0.577045044Subproblem 2
x + 1.444444445 = -2.021489489 Simplifying x + 1.444444445 = -2.021489489 Reorder the terms: 1.444444445 + x = -2.021489489 Solving 1.444444445 + x = -2.021489489 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 = -2.021489489 + -1.444444445 Combine like terms: 1.444444445 + -1.444444445 = 0.000000000 0.000000000 + x = -2.021489489 + -1.444444445 x = -2.021489489 + -1.444444445 Combine like terms: -2.021489489 + -1.444444445 = -3.465933934 x = -3.465933934 Simplifying x = -3.465933934Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.577045044, -3.465933934}
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