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Simplifying 11x2 + -2 = 7x Reorder the terms: -2 + 11x2 = 7x Solving -2 + 11x2 = 7x Solving for variable 'x'. Reorder the terms: -2 + -7x + 11x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -2 + -7x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.1818181818 + -0.6363636364x + x2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + -0.6363636364x + 0.1818181818 + x2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + -0.6363636364x + x2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + -0.6363636364x + x2 = 0 + 0.1818181818 -0.6363636364x + x2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 -0.6363636364x + x2 = 0.1818181818 The x term is -0.6363636364x. Take half its coefficient (-0.3181818182). Square it (0.1012396694) and add it to both sides. Add '0.1012396694' to each side of the equation. -0.6363636364x + 0.1012396694 + x2 = 0.1818181818 + 0.1012396694 Reorder the terms: 0.1012396694 + -0.6363636364x + x2 = 0.1818181818 + 0.1012396694 Combine like terms: 0.1818181818 + 0.1012396694 = 0.2830578512 0.1012396694 + -0.6363636364x + x2 = 0.2830578512 Factor a perfect square on the left side: (x + -0.3181818182)(x + -0.3181818182) = 0.2830578512 Calculate the square root of the right side: 0.532031814 Break this problem into two subproblems by setting (x + -0.3181818182) equal to 0.532031814 and -0.532031814.Subproblem 1
x + -0.3181818182 = 0.532031814 Simplifying x + -0.3181818182 = 0.532031814 Reorder the terms: -0.3181818182 + x = 0.532031814 Solving -0.3181818182 + x = 0.532031814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + x = 0.532031814 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = 0.532031814 + 0.3181818182 x = 0.532031814 + 0.3181818182 Combine like terms: 0.532031814 + 0.3181818182 = 0.8502136322 x = 0.8502136322 Simplifying x = 0.8502136322Subproblem 2
x + -0.3181818182 = -0.532031814 Simplifying x + -0.3181818182 = -0.532031814 Reorder the terms: -0.3181818182 + x = -0.532031814 Solving -0.3181818182 + x = -0.532031814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + x = -0.532031814 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = -0.532031814 + 0.3181818182 x = -0.532031814 + 0.3181818182 Combine like terms: -0.532031814 + 0.3181818182 = -0.2138499958 x = -0.2138499958 Simplifying x = -0.2138499958Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8502136322, -0.2138499958}
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