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Simplifying 11x2 + -1 + -7x = 0 Reorder the terms: -1 + -7x + 11x2 = 0 Solving -1 + -7x + 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'. -0.09090909091 + -0.6363636364x + x2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + -0.6363636364x + 0.09090909091 + x2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + -0.6363636364x + x2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + -0.6363636364x + x2 = 0 + 0.09090909091 -0.6363636364x + x2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 -0.6363636364x + x2 = 0.09090909091 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 = 0.09090909091 + 0.1012396694 Reorder the terms: 0.1012396694 + -0.6363636364x + x2 = 0.09090909091 + 0.1012396694 Combine like terms: 0.09090909091 + 0.1012396694 = 0.19214876031 0.1012396694 + -0.6363636364x + x2 = 0.19214876031 Factor a perfect square on the left side: (x + -0.3181818182)(x + -0.3181818182) = 0.19214876031 Calculate the square root of the right side: 0.438347762 Break this problem into two subproblems by setting (x + -0.3181818182) equal to 0.438347762 and -0.438347762.Subproblem 1
x + -0.3181818182 = 0.438347762 Simplifying x + -0.3181818182 = 0.438347762 Reorder the terms: -0.3181818182 + x = 0.438347762 Solving -0.3181818182 + x = 0.438347762 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 = 0.438347762 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = 0.438347762 + 0.3181818182 x = 0.438347762 + 0.3181818182 Combine like terms: 0.438347762 + 0.3181818182 = 0.7565295802 x = 0.7565295802 Simplifying x = 0.7565295802Subproblem 2
x + -0.3181818182 = -0.438347762 Simplifying x + -0.3181818182 = -0.438347762 Reorder the terms: -0.3181818182 + x = -0.438347762 Solving -0.3181818182 + x = -0.438347762 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 = -0.438347762 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = -0.438347762 + 0.3181818182 x = -0.438347762 + 0.3181818182 Combine like terms: -0.438347762 + 0.3181818182 = -0.1201659438 x = -0.1201659438 Simplifying x = -0.1201659438Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7565295802, -0.1201659438}
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