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Simplifying 13x2 + 22x + 5 = 0 Reorder the terms: 5 + 22x + 13x2 = 0 Solving 5 + 22x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.3846153846 + 1.692307692x + x2 = 0 Move the constant term to the right: Add '-0.3846153846' to each side of the equation. 0.3846153846 + 1.692307692x + -0.3846153846 + x2 = 0 + -0.3846153846 Reorder the terms: 0.3846153846 + -0.3846153846 + 1.692307692x + x2 = 0 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + 1.692307692x + x2 = 0 + -0.3846153846 1.692307692x + x2 = 0 + -0.3846153846 Combine like terms: 0 + -0.3846153846 = -0.3846153846 1.692307692x + x2 = -0.3846153846 The x term is 1.692307692x. Take half its coefficient (0.846153846). Square it (0.7159763311) and add it to both sides. Add '0.7159763311' to each side of the equation. 1.692307692x + 0.7159763311 + x2 = -0.3846153846 + 0.7159763311 Reorder the terms: 0.7159763311 + 1.692307692x + x2 = -0.3846153846 + 0.7159763311 Combine like terms: -0.3846153846 + 0.7159763311 = 0.3313609465 0.7159763311 + 1.692307692x + x2 = 0.3313609465 Factor a perfect square on the left side: (x + 0.846153846)(x + 0.846153846) = 0.3313609465 Calculate the square root of the right side: 0.575639598 Break this problem into two subproblems by setting (x + 0.846153846) equal to 0.575639598 and -0.575639598.Subproblem 1
x + 0.846153846 = 0.575639598 Simplifying x + 0.846153846 = 0.575639598 Reorder the terms: 0.846153846 + x = 0.575639598 Solving 0.846153846 + x = 0.575639598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.846153846' to each side of the equation. 0.846153846 + -0.846153846 + x = 0.575639598 + -0.846153846 Combine like terms: 0.846153846 + -0.846153846 = 0.000000000 0.000000000 + x = 0.575639598 + -0.846153846 x = 0.575639598 + -0.846153846 Combine like terms: 0.575639598 + -0.846153846 = -0.270514248 x = -0.270514248 Simplifying x = -0.270514248Subproblem 2
x + 0.846153846 = -0.575639598 Simplifying x + 0.846153846 = -0.575639598 Reorder the terms: 0.846153846 + x = -0.575639598 Solving 0.846153846 + x = -0.575639598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.846153846' to each side of the equation. 0.846153846 + -0.846153846 + x = -0.575639598 + -0.846153846 Combine like terms: 0.846153846 + -0.846153846 = 0.000000000 0.000000000 + x = -0.575639598 + -0.846153846 x = -0.575639598 + -0.846153846 Combine like terms: -0.575639598 + -0.846153846 = -1.421793444 x = -1.421793444 Simplifying x = -1.421793444Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.270514248, -1.421793444}
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