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Simplifying 11X2 + 6X + -20 = 0 Reorder the terms: -20 + 6X + 11X2 = 0 Solving -20 + 6X + 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'. -1.818181818 + 0.5454545455X + X2 = 0 Move the constant term to the right: Add '1.818181818' to each side of the equation. -1.818181818 + 0.5454545455X + 1.818181818 + X2 = 0 + 1.818181818 Reorder the terms: -1.818181818 + 1.818181818 + 0.5454545455X + X2 = 0 + 1.818181818 Combine like terms: -1.818181818 + 1.818181818 = 0.000000000 0.000000000 + 0.5454545455X + X2 = 0 + 1.818181818 0.5454545455X + X2 = 0 + 1.818181818 Combine like terms: 0 + 1.818181818 = 1.818181818 0.5454545455X + X2 = 1.818181818 The X term is 0.5454545455X. Take half its coefficient (0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. 0.5454545455X + 0.07438016533 + X2 = 1.818181818 + 0.07438016533 Reorder the terms: 0.07438016533 + 0.5454545455X + X2 = 1.818181818 + 0.07438016533 Combine like terms: 1.818181818 + 0.07438016533 = 1.89256198333 0.07438016533 + 0.5454545455X + X2 = 1.89256198333 Factor a perfect square on the left side: (X + 0.2727272728)(X + 0.2727272728) = 1.89256198333 Calculate the square root of the right side: 1.375704177 Break this problem into two subproblems by setting (X + 0.2727272728) equal to 1.375704177 and -1.375704177.Subproblem 1
X + 0.2727272728 = 1.375704177 Simplifying X + 0.2727272728 = 1.375704177 Reorder the terms: 0.2727272728 + X = 1.375704177 Solving 0.2727272728 + X = 1.375704177 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + X = 1.375704177 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + X = 1.375704177 + -0.2727272728 X = 1.375704177 + -0.2727272728 Combine like terms: 1.375704177 + -0.2727272728 = 1.1029769042 X = 1.1029769042 Simplifying X = 1.1029769042Subproblem 2
X + 0.2727272728 = -1.375704177 Simplifying X + 0.2727272728 = -1.375704177 Reorder the terms: 0.2727272728 + X = -1.375704177 Solving 0.2727272728 + X = -1.375704177 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + X = -1.375704177 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + X = -1.375704177 + -0.2727272728 X = -1.375704177 + -0.2727272728 Combine like terms: -1.375704177 + -0.2727272728 = -1.6484314498 X = -1.6484314498 Simplifying X = -1.6484314498Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.1029769042, -1.6484314498}
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