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Simplifying 6x2 + -17x + -11 = 0 Reorder the terms: -11 + -17x + 6x2 = 0 Solving -11 + -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'. -1.833333333 + -2.833333333x + x2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + -2.833333333x + 1.833333333 + x2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + -2.833333333x + x2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + -2.833333333x + x2 = 0 + 1.833333333 -2.833333333x + x2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 -2.833333333x + x2 = 1.833333333 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 = 1.833333333 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333x + x2 = 1.833333333 + 2.006944445 Combine like terms: 1.833333333 + 2.006944445 = 3.840277778 2.006944445 + -2.833333333x + x2 = 3.840277778 Factor a perfect square on the left side: (x + -1.416666667)(x + -1.416666667) = 3.840277778 Calculate the square root of the right side: 1.959662669 Break this problem into two subproblems by setting (x + -1.416666667) equal to 1.959662669 and -1.959662669.Subproblem 1
x + -1.416666667 = 1.959662669 Simplifying x + -1.416666667 = 1.959662669 Reorder the terms: -1.416666667 + x = 1.959662669 Solving -1.416666667 + x = 1.959662669 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 = 1.959662669 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = 1.959662669 + 1.416666667 x = 1.959662669 + 1.416666667 Combine like terms: 1.959662669 + 1.416666667 = 3.376329336 x = 3.376329336 Simplifying x = 3.376329336Subproblem 2
x + -1.416666667 = -1.959662669 Simplifying x + -1.416666667 = -1.959662669 Reorder the terms: -1.416666667 + x = -1.959662669 Solving -1.416666667 + x = -1.959662669 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 = -1.959662669 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = -1.959662669 + 1.416666667 x = -1.959662669 + 1.416666667 Combine like terms: -1.959662669 + 1.416666667 = -0.542996002 x = -0.542996002 Simplifying x = -0.542996002Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.376329336, -0.542996002}
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