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Simplifying 39y2 + -3y + -8 = 0 Reorder the terms: -8 + -3y + 39y2 = 0 Solving -8 + -3y + 39y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 39 the coefficient of the squared term: Divide each side by '39'. -0.2051282051 + -0.07692307692y + y2 = 0 Move the constant term to the right: Add '0.2051282051' to each side of the equation. -0.2051282051 + -0.07692307692y + 0.2051282051 + y2 = 0 + 0.2051282051 Reorder the terms: -0.2051282051 + 0.2051282051 + -0.07692307692y + y2 = 0 + 0.2051282051 Combine like terms: -0.2051282051 + 0.2051282051 = 0.0000000000 0.0000000000 + -0.07692307692y + y2 = 0 + 0.2051282051 -0.07692307692y + y2 = 0 + 0.2051282051 Combine like terms: 0 + 0.2051282051 = 0.2051282051 -0.07692307692y + y2 = 0.2051282051 The y term is -0.07692307692y. Take half its coefficient (-0.03846153846). Square it (0.001479289941) and add it to both sides. Add '0.001479289941' to each side of the equation. -0.07692307692y + 0.001479289941 + y2 = 0.2051282051 + 0.001479289941 Reorder the terms: 0.001479289941 + -0.07692307692y + y2 = 0.2051282051 + 0.001479289941 Combine like terms: 0.2051282051 + 0.001479289941 = 0.206607495041 0.001479289941 + -0.07692307692y + y2 = 0.206607495041 Factor a perfect square on the left side: (y + -0.03846153846)(y + -0.03846153846) = 0.206607495041 Calculate the square root of the right side: 0.454540972 Break this problem into two subproblems by setting (y + -0.03846153846) equal to 0.454540972 and -0.454540972.Subproblem 1
y + -0.03846153846 = 0.454540972 Simplifying y + -0.03846153846 = 0.454540972 Reorder the terms: -0.03846153846 + y = 0.454540972 Solving -0.03846153846 + y = 0.454540972 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.03846153846' to each side of the equation. -0.03846153846 + 0.03846153846 + y = 0.454540972 + 0.03846153846 Combine like terms: -0.03846153846 + 0.03846153846 = 0.00000000000 0.00000000000 + y = 0.454540972 + 0.03846153846 y = 0.454540972 + 0.03846153846 Combine like terms: 0.454540972 + 0.03846153846 = 0.49300251046 y = 0.49300251046 Simplifying y = 0.49300251046Subproblem 2
y + -0.03846153846 = -0.454540972 Simplifying y + -0.03846153846 = -0.454540972 Reorder the terms: -0.03846153846 + y = -0.454540972 Solving -0.03846153846 + y = -0.454540972 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.03846153846' to each side of the equation. -0.03846153846 + 0.03846153846 + y = -0.454540972 + 0.03846153846 Combine like terms: -0.03846153846 + 0.03846153846 = 0.00000000000 0.00000000000 + y = -0.454540972 + 0.03846153846 y = -0.454540972 + 0.03846153846 Combine like terms: -0.454540972 + 0.03846153846 = -0.41607943354 y = -0.41607943354 Simplifying y = -0.41607943354Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.49300251046, -0.41607943354}
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