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Simplifying 11x2 = 7x + 10 Reorder the terms: 11x2 = 10 + 7x Solving 11x2 = 10 + 7x Solving for variable 'x'. Reorder the terms: -10 + -7x + 11x2 = 10 + 7x + -10 + -7x Reorder the terms: -10 + -7x + 11x2 = 10 + -10 + 7x + -7x Combine like terms: 10 + -10 = 0 -10 + -7x + 11x2 = 0 + 7x + -7x -10 + -7x + 11x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -10 + -7x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.9090909091 + -0.6363636364x + x2 = 0 Move the constant term to the right: Add '0.9090909091' to each side of the equation. -0.9090909091 + -0.6363636364x + 0.9090909091 + x2 = 0 + 0.9090909091 Reorder the terms: -0.9090909091 + 0.9090909091 + -0.6363636364x + x2 = 0 + 0.9090909091 Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000 0.0000000000 + -0.6363636364x + x2 = 0 + 0.9090909091 -0.6363636364x + x2 = 0 + 0.9090909091 Combine like terms: 0 + 0.9090909091 = 0.9090909091 -0.6363636364x + x2 = 0.9090909091 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 = 0.9090909091 + 0.1012396694 Reorder the terms: 0.1012396694 + -0.6363636364x + x2 = 0.9090909091 + 0.1012396694 Combine like terms: 0.9090909091 + 0.1012396694 = 1.0103305785 0.1012396694 + -0.6363636364x + x2 = 1.0103305785 Factor a perfect square on the left side: (x + -0.3181818182)(x + -0.3181818182) = 1.0103305785 Calculate the square root of the right side: 1.005152018 Break this problem into two subproblems by setting (x + -0.3181818182) equal to 1.005152018 and -1.005152018.Subproblem 1
x + -0.3181818182 = 1.005152018 Simplifying x + -0.3181818182 = 1.005152018 Reorder the terms: -0.3181818182 + x = 1.005152018 Solving -0.3181818182 + x = 1.005152018 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 = 1.005152018 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = 1.005152018 + 0.3181818182 x = 1.005152018 + 0.3181818182 Combine like terms: 1.005152018 + 0.3181818182 = 1.3233338362 x = 1.3233338362 Simplifying x = 1.3233338362Subproblem 2
x + -0.3181818182 = -1.005152018 Simplifying x + -0.3181818182 = -1.005152018 Reorder the terms: -0.3181818182 + x = -1.005152018 Solving -0.3181818182 + x = -1.005152018 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 = -1.005152018 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = -1.005152018 + 0.3181818182 x = -1.005152018 + 0.3181818182 Combine like terms: -1.005152018 + 0.3181818182 = -0.6869701998 x = -0.6869701998 Simplifying x = -0.6869701998Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3233338362, -0.6869701998}
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