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Simplifying 6y2 + -14y + -30 = 0 Reorder the terms: -30 + -14y + 6y2 = 0 Solving -30 + -14y + 6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -7y + 3y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -7y + 3y2)' equal to zero and attempt to solve: Simplifying -15 + -7y + 3y2 = 0 Solving -15 + -7y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + -2.333333333y + y2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -2.333333333y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + -2.333333333y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2.333333333y + y2 = 0 + 5 -2.333333333y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2.333333333y + y2 = 5 The y term is -2.333333333y. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333y + 1.361111112 + y2 = 5 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333y + y2 = 5 + 1.361111112 Combine like terms: 5 + 1.361111112 = 6.361111112 1.361111112 + -2.333333333y + y2 = 6.361111112 Factor a perfect square on the left side: (y + -1.166666667)(y + -1.166666667) = 6.361111112 Calculate the square root of the right side: 2.522124325 Break this problem into two subproblems by setting (y + -1.166666667) equal to 2.522124325 and -2.522124325.Subproblem 1
y + -1.166666667 = 2.522124325 Simplifying y + -1.166666667 = 2.522124325 Reorder the terms: -1.166666667 + y = 2.522124325 Solving -1.166666667 + y = 2.522124325 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + y = 2.522124325 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + y = 2.522124325 + 1.166666667 y = 2.522124325 + 1.166666667 Combine like terms: 2.522124325 + 1.166666667 = 3.688790992 y = 3.688790992 Simplifying y = 3.688790992Subproblem 2
y + -1.166666667 = -2.522124325 Simplifying y + -1.166666667 = -2.522124325 Reorder the terms: -1.166666667 + y = -2.522124325 Solving -1.166666667 + y = -2.522124325 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + y = -2.522124325 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + y = -2.522124325 + 1.166666667 y = -2.522124325 + 1.166666667 Combine like terms: -2.522124325 + 1.166666667 = -1.355457658 y = -1.355457658 Simplifying y = -1.355457658Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.688790992, -1.355457658}Solution
y = {3.688790992, -1.355457658}
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