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Simplifying 51y2 + -30y + -15 = 0 Reorder the terms: -15 + -30y + 51y2 = 0 Solving -15 + -30y + 51y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + -10y + 17y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -10y + 17y2)' equal to zero and attempt to solve: Simplifying -5 + -10y + 17y2 = 0 Solving -5 + -10y + 17y2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.2941176471 + -0.5882352941y + y2 = 0 Move the constant term to the right: Add '0.2941176471' to each side of the equation. -0.2941176471 + -0.5882352941y + 0.2941176471 + y2 = 0 + 0.2941176471 Reorder the terms: -0.2941176471 + 0.2941176471 + -0.5882352941y + y2 = 0 + 0.2941176471 Combine like terms: -0.2941176471 + 0.2941176471 = 0.0000000000 0.0000000000 + -0.5882352941y + y2 = 0 + 0.2941176471 -0.5882352941y + y2 = 0 + 0.2941176471 Combine like terms: 0 + 0.2941176471 = 0.2941176471 -0.5882352941y + y2 = 0.2941176471 The y term is -0.5882352941y. Take half its coefficient (-0.2941176471). Square it (0.08650519034) and add it to both sides. Add '0.08650519034' to each side of the equation. -0.5882352941y + 0.08650519034 + y2 = 0.2941176471 + 0.08650519034 Reorder the terms: 0.08650519034 + -0.5882352941y + y2 = 0.2941176471 + 0.08650519034 Combine like terms: 0.2941176471 + 0.08650519034 = 0.38062283744 0.08650519034 + -0.5882352941y + y2 = 0.38062283744 Factor a perfect square on the left side: (y + -0.2941176471)(y + -0.2941176471) = 0.38062283744 Calculate the square root of the right side: 0.616946381 Break this problem into two subproblems by setting (y + -0.2941176471) equal to 0.616946381 and -0.616946381.Subproblem 1
y + -0.2941176471 = 0.616946381 Simplifying y + -0.2941176471 = 0.616946381 Reorder the terms: -0.2941176471 + y = 0.616946381 Solving -0.2941176471 + y = 0.616946381 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2941176471' to each side of the equation. -0.2941176471 + 0.2941176471 + y = 0.616946381 + 0.2941176471 Combine like terms: -0.2941176471 + 0.2941176471 = 0.0000000000 0.0000000000 + y = 0.616946381 + 0.2941176471 y = 0.616946381 + 0.2941176471 Combine like terms: 0.616946381 + 0.2941176471 = 0.9110640281 y = 0.9110640281 Simplifying y = 0.9110640281Subproblem 2
y + -0.2941176471 = -0.616946381 Simplifying y + -0.2941176471 = -0.616946381 Reorder the terms: -0.2941176471 + y = -0.616946381 Solving -0.2941176471 + y = -0.616946381 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2941176471' to each side of the equation. -0.2941176471 + 0.2941176471 + y = -0.616946381 + 0.2941176471 Combine like terms: -0.2941176471 + 0.2941176471 = 0.0000000000 0.0000000000 + y = -0.616946381 + 0.2941176471 y = -0.616946381 + 0.2941176471 Combine like terms: -0.616946381 + 0.2941176471 = -0.3228287339 y = -0.3228287339 Simplifying y = -0.3228287339Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.9110640281, -0.3228287339}Solution
y = {0.9110640281, -0.3228287339}
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