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Simplifying 9x2 + -26x = -18 Reorder the terms: -26x + 9x2 = -18 Solving -26x + 9x2 = -18 Solving for variable 'x'. Reorder the terms: 18 + -26x + 9x2 = -18 + 18 Combine like terms: -18 + 18 = 0 18 + -26x + 9x2 = 0 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 = 0.086419755 2.086419755 + -2.888888889x + x2 = 0.086419755 Factor a perfect square on the left side: (x + -1.444444445)(x + -1.444444445) = 0.086419755 Calculate the square root of the right side: 0.293972371 Break this problem into two subproblems by setting (x + -1.444444445) equal to 0.293972371 and -0.293972371.Subproblem 1
x + -1.444444445 = 0.293972371 Simplifying x + -1.444444445 = 0.293972371 Reorder the terms: -1.444444445 + x = 0.293972371 Solving -1.444444445 + x = 0.293972371 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 = 0.293972371 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + x = 0.293972371 + 1.444444445 x = 0.293972371 + 1.444444445 Combine like terms: 0.293972371 + 1.444444445 = 1.738416816 x = 1.738416816 Simplifying x = 1.738416816Subproblem 2
x + -1.444444445 = -0.293972371 Simplifying x + -1.444444445 = -0.293972371 Reorder the terms: -1.444444445 + x = -0.293972371 Solving -1.444444445 + x = -0.293972371 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 = -0.293972371 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + x = -0.293972371 + 1.444444445 x = -0.293972371 + 1.444444445 Combine like terms: -0.293972371 + 1.444444445 = 1.150472074 x = 1.150472074 Simplifying x = 1.150472074Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.738416816, 1.150472074}
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