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Simplifying 12y2 + -10y = 24 Reorder the terms: -10y + 12y2 = 24 Solving -10y + 12y2 = 24 Solving for variable 'y'. Reorder the terms: -24 + -10y + 12y2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -10y + 12y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -5y + 6y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -5y + 6y2)' equal to zero and attempt to solve: Simplifying -12 + -5y + 6y2 = 0 Solving -12 + -5y + 6y2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2 + -0.8333333333y + y2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.8333333333y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + -0.8333333333y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.8333333333y + y2 = 0 + 2 -0.8333333333y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.8333333333y + y2 = 2 The y term is -0.8333333333y. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333y + 0.1736111111 + y2 = 2 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333y + y2 = 2 + 0.1736111111 Combine like terms: 2 + 0.1736111111 = 2.1736111111 0.1736111111 + -0.8333333333y + y2 = 2.1736111111 Factor a perfect square on the left side: (y + -0.4166666667)(y + -0.4166666667) = 2.1736111111 Calculate the square root of the right side: 1.474317168 Break this problem into two subproblems by setting (y + -0.4166666667) equal to 1.474317168 and -1.474317168.Subproblem 1
y + -0.4166666667 = 1.474317168 Simplifying y + -0.4166666667 = 1.474317168 Reorder the terms: -0.4166666667 + y = 1.474317168 Solving -0.4166666667 + y = 1.474317168 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + y = 1.474317168 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + y = 1.474317168 + 0.4166666667 y = 1.474317168 + 0.4166666667 Combine like terms: 1.474317168 + 0.4166666667 = 1.8909838347 y = 1.8909838347 Simplifying y = 1.8909838347Subproblem 2
y + -0.4166666667 = -1.474317168 Simplifying y + -0.4166666667 = -1.474317168 Reorder the terms: -0.4166666667 + y = -1.474317168 Solving -0.4166666667 + y = -1.474317168 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + y = -1.474317168 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + y = -1.474317168 + 0.4166666667 y = -1.474317168 + 0.4166666667 Combine like terms: -1.474317168 + 0.4166666667 = -1.0576505013 y = -1.0576505013 Simplifying y = -1.0576505013Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.8909838347, -1.0576505013}Solution
y = {1.8909838347, -1.0576505013}
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