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Simplifying 13x2 + 10x + -1 = 0 Reorder the terms: -1 + 10x + 13x2 = 0 Solving -1 + 10x + 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'. -0.07692307692 + 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 = 0.22485207102 0.1479289941 + 0.7692307692x + x2 = 0.22485207102 Factor a perfect square on the left side: (x + 0.3846153846)(x + 0.3846153846) = 0.22485207102 Calculate the square root of the right side: 0.474185693 Break this problem into two subproblems by setting (x + 0.3846153846) equal to 0.474185693 and -0.474185693.Subproblem 1
x + 0.3846153846 = 0.474185693 Simplifying x + 0.3846153846 = 0.474185693 Reorder the terms: 0.3846153846 + x = 0.474185693 Solving 0.3846153846 + x = 0.474185693 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 = 0.474185693 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + x = 0.474185693 + -0.3846153846 x = 0.474185693 + -0.3846153846 Combine like terms: 0.474185693 + -0.3846153846 = 0.0895703084 x = 0.0895703084 Simplifying x = 0.0895703084Subproblem 2
x + 0.3846153846 = -0.474185693 Simplifying x + 0.3846153846 = -0.474185693 Reorder the terms: 0.3846153846 + x = -0.474185693 Solving 0.3846153846 + x = -0.474185693 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 = -0.474185693 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + x = -0.474185693 + -0.3846153846 x = -0.474185693 + -0.3846153846 Combine like terms: -0.474185693 + -0.3846153846 = -0.8588010776 x = -0.8588010776 Simplifying x = -0.8588010776Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0895703084, -0.8588010776}
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