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Simplifying 6x2 + -17x + 3 = 0 Reorder the terms: 3 + -17x + 6x2 = 0 Solving 3 + -17x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.5 + -2.833333333x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -2.833333333x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -2.833333333x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -2.833333333x + x2 = 0 + -0.5 -2.833333333x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -2.833333333x + x2 = -0.5 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 = -0.5 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333x + x2 = -0.5 + 2.006944445 Combine like terms: -0.5 + 2.006944445 = 1.506944445 2.006944445 + -2.833333333x + x2 = 1.506944445 Factor a perfect square on the left side: (x + -1.416666667)(x + -1.416666667) = 1.506944445 Calculate the square root of the right side: 1.227576655 Break this problem into two subproblems by setting (x + -1.416666667) equal to 1.227576655 and -1.227576655.Subproblem 1
x + -1.416666667 = 1.227576655 Simplifying x + -1.416666667 = 1.227576655 Reorder the terms: -1.416666667 + x = 1.227576655 Solving -1.416666667 + x = 1.227576655 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 = 1.227576655 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = 1.227576655 + 1.416666667 x = 1.227576655 + 1.416666667 Combine like terms: 1.227576655 + 1.416666667 = 2.644243322 x = 2.644243322 Simplifying x = 2.644243322Subproblem 2
x + -1.416666667 = -1.227576655 Simplifying x + -1.416666667 = -1.227576655 Reorder the terms: -1.416666667 + x = -1.227576655 Solving -1.416666667 + x = -1.227576655 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 = -1.227576655 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = -1.227576655 + 1.416666667 x = -1.227576655 + 1.416666667 Combine like terms: -1.227576655 + 1.416666667 = 0.189090012 x = 0.189090012 Simplifying x = 0.189090012Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.644243322, 0.189090012}
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