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Simplifying 11x(6x + -11) = 1 + 4x Reorder the terms: 11x(-11 + 6x) = 1 + 4x (-11 * 11x + 6x * 11x) = 1 + 4x (-121x + 66x2) = 1 + 4x Solving -121x + 66x2 = 1 + 4x Solving for variable 'x'. Reorder the terms: -1 + -121x + -4x + 66x2 = 1 + 4x + -1 + -4x Combine like terms: -121x + -4x = -125x -1 + -125x + 66x2 = 1 + 4x + -1 + -4x Reorder the terms: -1 + -125x + 66x2 = 1 + -1 + 4x + -4x Combine like terms: 1 + -1 = 0 -1 + -125x + 66x2 = 0 + 4x + -4x -1 + -125x + 66x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -1 + -125x + 66x2 = 0 Begin completing the square. Divide all terms by 66 the coefficient of the squared term: Divide each side by '66'. -0.01515151515 + -1.893939394x + x2 = 0 Move the constant term to the right: Add '0.01515151515' to each side of the equation. -0.01515151515 + -1.893939394x + 0.01515151515 + x2 = 0 + 0.01515151515 Reorder the terms: -0.01515151515 + 0.01515151515 + -1.893939394x + x2 = 0 + 0.01515151515 Combine like terms: -0.01515151515 + 0.01515151515 = 0.00000000000 0.00000000000 + -1.893939394x + x2 = 0 + 0.01515151515 -1.893939394x + x2 = 0 + 0.01515151515 Combine like terms: 0 + 0.01515151515 = 0.01515151515 -1.893939394x + x2 = 0.01515151515 The x term is -1.893939394x. Take half its coefficient (-0.946969697). Square it (0.8967516070) and add it to both sides. Add '0.8967516070' to each side of the equation. -1.893939394x + 0.8967516070 + x2 = 0.01515151515 + 0.8967516070 Reorder the terms: 0.8967516070 + -1.893939394x + x2 = 0.01515151515 + 0.8967516070 Combine like terms: 0.01515151515 + 0.8967516070 = 0.91190312215 0.8967516070 + -1.893939394x + x2 = 0.91190312215 Factor a perfect square on the left side: (x + -0.946969697)(x + -0.946969697) = 0.91190312215 Calculate the square root of the right side: 0.954936187 Break this problem into two subproblems by setting (x + -0.946969697) equal to 0.954936187 and -0.954936187.Subproblem 1
x + -0.946969697 = 0.954936187 Simplifying x + -0.946969697 = 0.954936187 Reorder the terms: -0.946969697 + x = 0.954936187 Solving -0.946969697 + x = 0.954936187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.946969697' to each side of the equation. -0.946969697 + 0.946969697 + x = 0.954936187 + 0.946969697 Combine like terms: -0.946969697 + 0.946969697 = 0.000000000 0.000000000 + x = 0.954936187 + 0.946969697 x = 0.954936187 + 0.946969697 Combine like terms: 0.954936187 + 0.946969697 = 1.901905884 x = 1.901905884 Simplifying x = 1.901905884Subproblem 2
x + -0.946969697 = -0.954936187 Simplifying x + -0.946969697 = -0.954936187 Reorder the terms: -0.946969697 + x = -0.954936187 Solving -0.946969697 + x = -0.954936187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.946969697' to each side of the equation. -0.946969697 + 0.946969697 + x = -0.954936187 + 0.946969697 Combine like terms: -0.946969697 + 0.946969697 = 0.000000000 0.000000000 + x = -0.954936187 + 0.946969697 x = -0.954936187 + 0.946969697 Combine like terms: -0.954936187 + 0.946969697 = -0.00796649 x = -0.00796649 Simplifying x = -0.00796649Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.901905884, -0.00796649}
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