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Simplifying 11X2 + 3X + -5 = 8 Reorder the terms: -5 + 3X + 11X2 = 8 Solving -5 + 3X + 11X2 = 8 Solving for variable 'X'. Reorder the terms: -5 + -8 + 3X + 11X2 = 8 + -8 Combine like terms: -5 + -8 = -13 -13 + 3X + 11X2 = 8 + -8 Combine like terms: 8 + -8 = 0 -13 + 3X + 11X2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.181818182 + 0.2727272727X + X2 = 0 Move the constant term to the right: Add '1.181818182' to each side of the equation. -1.181818182 + 0.2727272727X + 1.181818182 + X2 = 0 + 1.181818182 Reorder the terms: -1.181818182 + 1.181818182 + 0.2727272727X + X2 = 0 + 1.181818182 Combine like terms: -1.181818182 + 1.181818182 = 0.000000000 0.000000000 + 0.2727272727X + X2 = 0 + 1.181818182 0.2727272727X + X2 = 0 + 1.181818182 Combine like terms: 0 + 1.181818182 = 1.181818182 0.2727272727X + X2 = 1.181818182 The X term is 0.2727272727X. Take half its coefficient (0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. 0.2727272727X + 0.01859504133 + X2 = 1.181818182 + 0.01859504133 Reorder the terms: 0.01859504133 + 0.2727272727X + X2 = 1.181818182 + 0.01859504133 Combine like terms: 1.181818182 + 0.01859504133 = 1.20041322333 0.01859504133 + 0.2727272727X + X2 = 1.20041322333 Factor a perfect square on the left side: (X + 0.1363636364)(X + 0.1363636364) = 1.20041322333 Calculate the square root of the right side: 1.095633709 Break this problem into two subproblems by setting (X + 0.1363636364) equal to 1.095633709 and -1.095633709.Subproblem 1
X + 0.1363636364 = 1.095633709 Simplifying X + 0.1363636364 = 1.095633709 Reorder the terms: 0.1363636364 + X = 1.095633709 Solving 0.1363636364 + X = 1.095633709 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + X = 1.095633709 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + X = 1.095633709 + -0.1363636364 X = 1.095633709 + -0.1363636364 Combine like terms: 1.095633709 + -0.1363636364 = 0.9592700726 X = 0.9592700726 Simplifying X = 0.9592700726Subproblem 2
X + 0.1363636364 = -1.095633709 Simplifying X + 0.1363636364 = -1.095633709 Reorder the terms: 0.1363636364 + X = -1.095633709 Solving 0.1363636364 + X = -1.095633709 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + X = -1.095633709 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + X = -1.095633709 + -0.1363636364 X = -1.095633709 + -0.1363636364 Combine like terms: -1.095633709 + -0.1363636364 = -1.2319973454 X = -1.2319973454 Simplifying X = -1.2319973454Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.9592700726, -1.2319973454}
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