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Simplifying 11x2 + -30x + 2 = 0 Reorder the terms: 2 + -30x + 11x2 = 0 Solving 2 + -30x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.1818181818 + -2.727272727x + x2 = 0 Move the constant term to the right: Add '-0.1818181818' to each side of the equation. 0.1818181818 + -2.727272727x + -0.1818181818 + x2 = 0 + -0.1818181818 Reorder the terms: 0.1818181818 + -0.1818181818 + -2.727272727x + x2 = 0 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + -2.727272727x + x2 = 0 + -0.1818181818 -2.727272727x + x2 = 0 + -0.1818181818 Combine like terms: 0 + -0.1818181818 = -0.1818181818 -2.727272727x + x2 = -0.1818181818 The x term is -2.727272727x. Take half its coefficient (-1.363636364). Square it (1.859504133) and add it to both sides. Add '1.859504133' to each side of the equation. -2.727272727x + 1.859504133 + x2 = -0.1818181818 + 1.859504133 Reorder the terms: 1.859504133 + -2.727272727x + x2 = -0.1818181818 + 1.859504133 Combine like terms: -0.1818181818 + 1.859504133 = 1.6776859512 1.859504133 + -2.727272727x + x2 = 1.6776859512 Factor a perfect square on the left side: (x + -1.363636364)(x + -1.363636364) = 1.6776859512 Calculate the square root of the right side: 1.295255168 Break this problem into two subproblems by setting (x + -1.363636364) equal to 1.295255168 and -1.295255168.Subproblem 1
x + -1.363636364 = 1.295255168 Simplifying x + -1.363636364 = 1.295255168 Reorder the terms: -1.363636364 + x = 1.295255168 Solving -1.363636364 + x = 1.295255168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.363636364' to each side of the equation. -1.363636364 + 1.363636364 + x = 1.295255168 + 1.363636364 Combine like terms: -1.363636364 + 1.363636364 = 0.000000000 0.000000000 + x = 1.295255168 + 1.363636364 x = 1.295255168 + 1.363636364 Combine like terms: 1.295255168 + 1.363636364 = 2.658891532 x = 2.658891532 Simplifying x = 2.658891532Subproblem 2
x + -1.363636364 = -1.295255168 Simplifying x + -1.363636364 = -1.295255168 Reorder the terms: -1.363636364 + x = -1.295255168 Solving -1.363636364 + x = -1.295255168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.363636364' to each side of the equation. -1.363636364 + 1.363636364 + x = -1.295255168 + 1.363636364 Combine like terms: -1.363636364 + 1.363636364 = 0.000000000 0.000000000 + x = -1.295255168 + 1.363636364 x = -1.295255168 + 1.363636364 Combine like terms: -1.295255168 + 1.363636364 = 0.068381196 x = 0.068381196 Simplifying x = 0.068381196Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.658891532, 0.068381196}
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