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Simplifying 11x2 + -12 = 7x Reorder the terms: -12 + 11x2 = 7x Solving -12 + 11x2 = 7x Solving for variable 'x'. Reorder the terms: -12 + -7x + 11x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -12 + -7x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.090909091 + -0.6363636364x + x2 = 0 Move the constant term to the right: Add '1.090909091' to each side of the equation. -1.090909091 + -0.6363636364x + 1.090909091 + x2 = 0 + 1.090909091 Reorder the terms: -1.090909091 + 1.090909091 + -0.6363636364x + x2 = 0 + 1.090909091 Combine like terms: -1.090909091 + 1.090909091 = 0.000000000 0.000000000 + -0.6363636364x + x2 = 0 + 1.090909091 -0.6363636364x + x2 = 0 + 1.090909091 Combine like terms: 0 + 1.090909091 = 1.090909091 -0.6363636364x + x2 = 1.090909091 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 = 1.090909091 + 0.1012396694 Reorder the terms: 0.1012396694 + -0.6363636364x + x2 = 1.090909091 + 0.1012396694 Combine like terms: 1.090909091 + 0.1012396694 = 1.1921487604 0.1012396694 + -0.6363636364x + x2 = 1.1921487604 Factor a perfect square on the left side: (x + -0.3181818182)(x + -0.3181818182) = 1.1921487604 Calculate the square root of the right side: 1.09185565 Break this problem into two subproblems by setting (x + -0.3181818182) equal to 1.09185565 and -1.09185565.Subproblem 1
x + -0.3181818182 = 1.09185565 Simplifying x + -0.3181818182 = 1.09185565 Reorder the terms: -0.3181818182 + x = 1.09185565 Solving -0.3181818182 + x = 1.09185565 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 = 1.09185565 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = 1.09185565 + 0.3181818182 x = 1.09185565 + 0.3181818182 Combine like terms: 1.09185565 + 0.3181818182 = 1.4100374682 x = 1.4100374682 Simplifying x = 1.4100374682Subproblem 2
x + -0.3181818182 = -1.09185565 Simplifying x + -0.3181818182 = -1.09185565 Reorder the terms: -0.3181818182 + x = -1.09185565 Solving -0.3181818182 + x = -1.09185565 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 = -1.09185565 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = -1.09185565 + 0.3181818182 x = -1.09185565 + 0.3181818182 Combine like terms: -1.09185565 + 0.3181818182 = -0.7736738318 x = -0.7736738318 Simplifying x = -0.7736738318Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4100374682, -0.7736738318}
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