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Simplifying 11x2 + 12x + -66 = 0 Reorder the terms: -66 + 12x + 11x2 = 0 Solving -66 + 12x + 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'. -6 + 1.090909091x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 1.090909091x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 1.090909091x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 1.090909091x + x2 = 0 + 6 1.090909091x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 1.090909091x + x2 = 6 The x term is 1.090909091x. Take half its coefficient (0.5454545455). Square it (0.2975206612) and add it to both sides. Add '0.2975206612' to each side of the equation. 1.090909091x + 0.2975206612 + x2 = 6 + 0.2975206612 Reorder the terms: 0.2975206612 + 1.090909091x + x2 = 6 + 0.2975206612 Combine like terms: 6 + 0.2975206612 = 6.2975206612 0.2975206612 + 1.090909091x + x2 = 6.2975206612 Factor a perfect square on the left side: (x + 0.5454545455)(x + 0.5454545455) = 6.2975206612 Calculate the square root of the right side: 2.509486135 Break this problem into two subproblems by setting (x + 0.5454545455) equal to 2.509486135 and -2.509486135.Subproblem 1
x + 0.5454545455 = 2.509486135 Simplifying x + 0.5454545455 = 2.509486135 Reorder the terms: 0.5454545455 + x = 2.509486135 Solving 0.5454545455 + x = 2.509486135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5454545455' to each side of the equation. 0.5454545455 + -0.5454545455 + x = 2.509486135 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + x = 2.509486135 + -0.5454545455 x = 2.509486135 + -0.5454545455 Combine like terms: 2.509486135 + -0.5454545455 = 1.9640315895 x = 1.9640315895 Simplifying x = 1.9640315895Subproblem 2
x + 0.5454545455 = -2.509486135 Simplifying x + 0.5454545455 = -2.509486135 Reorder the terms: 0.5454545455 + x = -2.509486135 Solving 0.5454545455 + x = -2.509486135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5454545455' to each side of the equation. 0.5454545455 + -0.5454545455 + x = -2.509486135 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + x = -2.509486135 + -0.5454545455 x = -2.509486135 + -0.5454545455 Combine like terms: -2.509486135 + -0.5454545455 = -3.0549406805 x = -3.0549406805 Simplifying x = -3.0549406805Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9640315895, -3.0549406805}
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