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Simplifying 13x2 + 1 = -10x Reorder the terms: 1 + 13x2 = -10x Solving 1 + 13x2 = -10x Solving for variable 'x'. Reorder the terms: 1 + 10x + 13x2 = -10x + 10x Combine like terms: -10x + 10x = 0 1 + 10x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.07692307692 + 0.7692307692x + x2 = 0 Move the constant term to the right: Add '-0.07692307692' to each side of the equation. 0.07692307692 + 0.7692307692x + -0.07692307692 + x2 = 0 + -0.07692307692 Reorder the terms: 0.07692307692 + -0.07692307692 + 0.7692307692x + x2 = 0 + -0.07692307692 Combine like terms: 0.07692307692 + -0.07692307692 = 0.00000000000 0.00000000000 + 0.7692307692x + x2 = 0 + -0.07692307692 0.7692307692x + x2 = 0 + -0.07692307692 Combine like terms: 0 + -0.07692307692 = -0.07692307692 0.7692307692x + x2 = -0.07692307692 The x term is 0.7692307692x. Take half its coefficient (0.3846153846). Square it (0.1479289941) and add it to both sides. Add '0.1479289941' to each side of the equation. 0.7692307692x + 0.1479289941 + x2 = -0.07692307692 + 0.1479289941 Reorder the terms: 0.1479289941 + 0.7692307692x + x2 = -0.07692307692 + 0.1479289941 Combine like terms: -0.07692307692 + 0.1479289941 = 0.07100591718 0.1479289941 + 0.7692307692x + x2 = 0.07100591718 Factor a perfect square on the left side: (x + 0.3846153846)(x + 0.3846153846) = 0.07100591718 Calculate the square root of the right side: 0.266469355 Break this problem into two subproblems by setting (x + 0.3846153846) equal to 0.266469355 and -0.266469355.Subproblem 1
x + 0.3846153846 = 0.266469355 Simplifying x + 0.3846153846 = 0.266469355 Reorder the terms: 0.3846153846 + x = 0.266469355 Solving 0.3846153846 + x = 0.266469355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3846153846' to each side of the equation. 0.3846153846 + -0.3846153846 + x = 0.266469355 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + x = 0.266469355 + -0.3846153846 x = 0.266469355 + -0.3846153846 Combine like terms: 0.266469355 + -0.3846153846 = -0.1181460296 x = -0.1181460296 Simplifying x = -0.1181460296Subproblem 2
x + 0.3846153846 = -0.266469355 Simplifying x + 0.3846153846 = -0.266469355 Reorder the terms: 0.3846153846 + x = -0.266469355 Solving 0.3846153846 + x = -0.266469355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3846153846' to each side of the equation. 0.3846153846 + -0.3846153846 + x = -0.266469355 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + x = -0.266469355 + -0.3846153846 x = -0.266469355 + -0.3846153846 Combine like terms: -0.266469355 + -0.3846153846 = -0.6510847396 x = -0.6510847396 Simplifying x = -0.6510847396Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1181460296, -0.6510847396}
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