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Simplifying 12y2 + -38y + 10 = 0 Reorder the terms: 10 + -38y + 12y2 = 0 Solving 10 + -38y + 12y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -19y + 6y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -19y + 6y2)' equal to zero and attempt to solve: Simplifying 5 + -19y + 6y2 = 0 Solving 5 + -19y + 6y2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + -3.166666667y + y2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -3.166666667y + -0.8333333333 + y2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -3.166666667y + y2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -3.166666667y + y2 = 0 + -0.8333333333 -3.166666667y + y2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -3.166666667y + y2 = -0.8333333333 The y term is -3.166666667y. Take half its coefficient (-1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. -3.166666667y + 2.506944447 + y2 = -0.8333333333 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667y + y2 = -0.8333333333 + 2.506944447 Combine like terms: -0.8333333333 + 2.506944447 = 1.6736111137 2.506944447 + -3.166666667y + y2 = 1.6736111137 Factor a perfect square on the left side: (y + -1.583333334)(y + -1.583333334) = 1.6736111137 Calculate the square root of the right side: 1.293681226 Break this problem into two subproblems by setting (y + -1.583333334) equal to 1.293681226 and -1.293681226.Subproblem 1
y + -1.583333334 = 1.293681226 Simplifying y + -1.583333334 = 1.293681226 Reorder the terms: -1.583333334 + y = 1.293681226 Solving -1.583333334 + y = 1.293681226 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + y = 1.293681226 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + y = 1.293681226 + 1.583333334 y = 1.293681226 + 1.583333334 Combine like terms: 1.293681226 + 1.583333334 = 2.87701456 y = 2.87701456 Simplifying y = 2.87701456Subproblem 2
y + -1.583333334 = -1.293681226 Simplifying y + -1.583333334 = -1.293681226 Reorder the terms: -1.583333334 + y = -1.293681226 Solving -1.583333334 + y = -1.293681226 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + y = -1.293681226 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + y = -1.293681226 + 1.583333334 y = -1.293681226 + 1.583333334 Combine like terms: -1.293681226 + 1.583333334 = 0.289652108 y = 0.289652108 Simplifying y = 0.289652108Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.87701456, 0.289652108}Solution
y = {2.87701456, 0.289652108}
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