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Simplifying 13x2 + 10x + -13 = 0 Reorder the terms: -13 + 10x + 13x2 = 0 Solving -13 + 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'. -1 + 0.7692307692x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.7692307692x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.7692307692x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.7692307692x + x2 = 0 + 1 0.7692307692x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.7692307692x + x2 = 1 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 = 1 + 0.1479289941 Reorder the terms: 0.1479289941 + 0.7692307692x + x2 = 1 + 0.1479289941 Combine like terms: 1 + 0.1479289941 = 1.1479289941 0.1479289941 + 0.7692307692x + x2 = 1.1479289941 Factor a perfect square on the left side: (x + 0.3846153846)(x + 0.3846153846) = 1.1479289941 Calculate the square root of the right side: 1.071414483 Break this problem into two subproblems by setting (x + 0.3846153846) equal to 1.071414483 and -1.071414483.Subproblem 1
x + 0.3846153846 = 1.071414483 Simplifying x + 0.3846153846 = 1.071414483 Reorder the terms: 0.3846153846 + x = 1.071414483 Solving 0.3846153846 + x = 1.071414483 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 = 1.071414483 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + x = 1.071414483 + -0.3846153846 x = 1.071414483 + -0.3846153846 Combine like terms: 1.071414483 + -0.3846153846 = 0.6867990984 x = 0.6867990984 Simplifying x = 0.6867990984Subproblem 2
x + 0.3846153846 = -1.071414483 Simplifying x + 0.3846153846 = -1.071414483 Reorder the terms: 0.3846153846 + x = -1.071414483 Solving 0.3846153846 + x = -1.071414483 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 = -1.071414483 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + x = -1.071414483 + -0.3846153846 x = -1.071414483 + -0.3846153846 Combine like terms: -1.071414483 + -0.3846153846 = -1.4560298676 x = -1.4560298676 Simplifying x = -1.4560298676Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6867990984, -1.4560298676}
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