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Simplifying 13y2 + -10y + 1 = 0 Reorder the terms: 1 + -10y + 13y2 = 0 Solving 1 + -10y + 13y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.07692307692 + -0.7692307692y + y2 = 0 Move the constant term to the right: Add '-0.07692307692' to each side of the equation. 0.07692307692 + -0.7692307692y + -0.07692307692 + y2 = 0 + -0.07692307692 Reorder the terms: 0.07692307692 + -0.07692307692 + -0.7692307692y + y2 = 0 + -0.07692307692 Combine like terms: 0.07692307692 + -0.07692307692 = 0.00000000000 0.00000000000 + -0.7692307692y + y2 = 0 + -0.07692307692 -0.7692307692y + y2 = 0 + -0.07692307692 Combine like terms: 0 + -0.07692307692 = -0.07692307692 -0.7692307692y + y2 = -0.07692307692 The y term is -0.7692307692y. 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. -0.7692307692y + 0.1479289941 + y2 = -0.07692307692 + 0.1479289941 Reorder the terms: 0.1479289941 + -0.7692307692y + y2 = -0.07692307692 + 0.1479289941 Combine like terms: -0.07692307692 + 0.1479289941 = 0.07100591718 0.1479289941 + -0.7692307692y + y2 = 0.07100591718 Factor a perfect square on the left side: (y + -0.3846153846)(y + -0.3846153846) = 0.07100591718 Calculate the square root of the right side: 0.266469355 Break this problem into two subproblems by setting (y + -0.3846153846) equal to 0.266469355 and -0.266469355.Subproblem 1
y + -0.3846153846 = 0.266469355 Simplifying y + -0.3846153846 = 0.266469355 Reorder the terms: -0.3846153846 + y = 0.266469355 Solving -0.3846153846 + y = 0.266469355 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3846153846' to each side of the equation. -0.3846153846 + 0.3846153846 + y = 0.266469355 + 0.3846153846 Combine like terms: -0.3846153846 + 0.3846153846 = 0.0000000000 0.0000000000 + y = 0.266469355 + 0.3846153846 y = 0.266469355 + 0.3846153846 Combine like terms: 0.266469355 + 0.3846153846 = 0.6510847396 y = 0.6510847396 Simplifying y = 0.6510847396Subproblem 2
y + -0.3846153846 = -0.266469355 Simplifying y + -0.3846153846 = -0.266469355 Reorder the terms: -0.3846153846 + y = -0.266469355 Solving -0.3846153846 + y = -0.266469355 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3846153846' to each side of the equation. -0.3846153846 + 0.3846153846 + y = -0.266469355 + 0.3846153846 Combine like terms: -0.3846153846 + 0.3846153846 = 0.0000000000 0.0000000000 + y = -0.266469355 + 0.3846153846 y = -0.266469355 + 0.3846153846 Combine like terms: -0.266469355 + 0.3846153846 = 0.1181460296 y = 0.1181460296 Simplifying y = 0.1181460296Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.6510847396, 0.1181460296}
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