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Simplifying 0 = -6x2 + 17x + -9 Reorder the terms: 0 = -9 + 17x + -6x2 Solving 0 = -9 + 17x + -6x2 Solving for variable 'x'. Combine like terms: 0 + 9 = 9 9 + -17x + 6x2 = -9 + 17x + -6x2 + 9 + -17x + 6x2 Reorder the terms: 9 + -17x + 6x2 = -9 + 9 + 17x + -17x + -6x2 + 6x2 Combine like terms: -9 + 9 = 0 9 + -17x + 6x2 = 0 + 17x + -17x + -6x2 + 6x2 9 + -17x + 6x2 = 17x + -17x + -6x2 + 6x2 Combine like terms: 17x + -17x = 0 9 + -17x + 6x2 = 0 + -6x2 + 6x2 9 + -17x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 9 + -17x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.5 + -2.833333333x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -2.833333333x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -2.833333333x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -2.833333333x + x2 = 0 + -1.5 -2.833333333x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -2.833333333x + x2 = -1.5 The x term is -2.833333333x. Take half its coefficient (-1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. -2.833333333x + 2.006944445 + x2 = -1.5 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333x + x2 = -1.5 + 2.006944445 Combine like terms: -1.5 + 2.006944445 = 0.506944445 2.006944445 + -2.833333333x + x2 = 0.506944445 Factor a perfect square on the left side: (x + -1.416666667)(x + -1.416666667) = 0.506944445 Calculate the square root of the right side: 0.712000313 Break this problem into two subproblems by setting (x + -1.416666667) equal to 0.712000313 and -0.712000313.Subproblem 1
x + -1.416666667 = 0.712000313 Simplifying x + -1.416666667 = 0.712000313 Reorder the terms: -1.416666667 + x = 0.712000313 Solving -1.416666667 + x = 0.712000313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = 0.712000313 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = 0.712000313 + 1.416666667 x = 0.712000313 + 1.416666667 Combine like terms: 0.712000313 + 1.416666667 = 2.12866698 x = 2.12866698 Simplifying x = 2.12866698Subproblem 2
x + -1.416666667 = -0.712000313 Simplifying x + -1.416666667 = -0.712000313 Reorder the terms: -1.416666667 + x = -0.712000313 Solving -1.416666667 + x = -0.712000313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = -0.712000313 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = -0.712000313 + 1.416666667 x = -0.712000313 + 1.416666667 Combine like terms: -0.712000313 + 1.416666667 = 0.704666354 x = 0.704666354 Simplifying x = 0.704666354Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.12866698, 0.704666354}
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