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Simplifying 11x2 + 7x + -10 = 5 Reorder the terms: -10 + 7x + 11x2 = 5 Solving -10 + 7x + 11x2 = 5 Solving for variable 'x'. Reorder the terms: -10 + -5 + 7x + 11x2 = 5 + -5 Combine like terms: -10 + -5 = -15 -15 + 7x + 11x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -15 + 7x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.363636364 + 0.6363636364x + x2 = 0 Move the constant term to the right: Add '1.363636364' to each side of the equation. -1.363636364 + 0.6363636364x + 1.363636364 + x2 = 0 + 1.363636364 Reorder the terms: -1.363636364 + 1.363636364 + 0.6363636364x + x2 = 0 + 1.363636364 Combine like terms: -1.363636364 + 1.363636364 = 0.000000000 0.000000000 + 0.6363636364x + x2 = 0 + 1.363636364 0.6363636364x + x2 = 0 + 1.363636364 Combine like terms: 0 + 1.363636364 = 1.363636364 0.6363636364x + x2 = 1.363636364 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 = 1.363636364 + 0.1012396694 Reorder the terms: 0.1012396694 + 0.6363636364x + x2 = 1.363636364 + 0.1012396694 Combine like terms: 1.363636364 + 0.1012396694 = 1.4648760334 0.1012396694 + 0.6363636364x + x2 = 1.4648760334 Factor a perfect square on the left side: (x + 0.3181818182)(x + 0.3181818182) = 1.4648760334 Calculate the square root of the right side: 1.210320632 Break this problem into two subproblems by setting (x + 0.3181818182) equal to 1.210320632 and -1.210320632.Subproblem 1
x + 0.3181818182 = 1.210320632 Simplifying x + 0.3181818182 = 1.210320632 Reorder the terms: 0.3181818182 + x = 1.210320632 Solving 0.3181818182 + x = 1.210320632 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 = 1.210320632 + -0.3181818182 Combine like terms: 0.3181818182 + -0.3181818182 = 0.0000000000 0.0000000000 + x = 1.210320632 + -0.3181818182 x = 1.210320632 + -0.3181818182 Combine like terms: 1.210320632 + -0.3181818182 = 0.8921388138 x = 0.8921388138 Simplifying x = 0.8921388138Subproblem 2
x + 0.3181818182 = -1.210320632 Simplifying x + 0.3181818182 = -1.210320632 Reorder the terms: 0.3181818182 + x = -1.210320632 Solving 0.3181818182 + x = -1.210320632 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 = -1.210320632 + -0.3181818182 Combine like terms: 0.3181818182 + -0.3181818182 = 0.0000000000 0.0000000000 + x = -1.210320632 + -0.3181818182 x = -1.210320632 + -0.3181818182 Combine like terms: -1.210320632 + -0.3181818182 = -1.5285024502 x = -1.5285024502 Simplifying x = -1.5285024502Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8921388138, -1.5285024502}
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