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Simplifying -4y(3y + -10) + 3(2y + 8) = 0 Reorder the terms: -4y(-10 + 3y) + 3(2y + 8) = 0 (-10 * -4y + 3y * -4y) + 3(2y + 8) = 0 (40y + -12y2) + 3(2y + 8) = 0 Reorder the terms: 40y + -12y2 + 3(8 + 2y) = 0 40y + -12y2 + (8 * 3 + 2y * 3) = 0 40y + -12y2 + (24 + 6y) = 0 Reorder the terms: 24 + 40y + 6y + -12y2 = 0 Combine like terms: 40y + 6y = 46y 24 + 46y + -12y2 = 0 Solving 24 + 46y + -12y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 23y + -6y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 23y + -6y2)' equal to zero and attempt to solve: Simplifying 12 + 23y + -6y2 = 0 Solving 12 + 23y + -6y2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -2 + -3.833333333y + y2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -3.833333333y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + -3.833333333y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3.833333333y + y2 = 0 + 2 -3.833333333y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3.833333333y + y2 = 2 The y term is -3.833333333y. Take half its coefficient (-1.916666667). Square it (3.673611112) and add it to both sides. Add '3.673611112' to each side of the equation. -3.833333333y + 3.673611112 + y2 = 2 + 3.673611112 Reorder the terms: 3.673611112 + -3.833333333y + y2 = 2 + 3.673611112 Combine like terms: 2 + 3.673611112 = 5.673611112 3.673611112 + -3.833333333y + y2 = 5.673611112 Factor a perfect square on the left side: (y + -1.916666667)(y + -1.916666667) = 5.673611112 Calculate the square root of the right side: 2.381934322 Break this problem into two subproblems by setting (y + -1.916666667) equal to 2.381934322 and -2.381934322.Subproblem 1
y + -1.916666667 = 2.381934322 Simplifying y + -1.916666667 = 2.381934322 Reorder the terms: -1.916666667 + y = 2.381934322 Solving -1.916666667 + y = 2.381934322 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + y = 2.381934322 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + y = 2.381934322 + 1.916666667 y = 2.381934322 + 1.916666667 Combine like terms: 2.381934322 + 1.916666667 = 4.298600989 y = 4.298600989 Simplifying y = 4.298600989Subproblem 2
y + -1.916666667 = -2.381934322 Simplifying y + -1.916666667 = -2.381934322 Reorder the terms: -1.916666667 + y = -2.381934322 Solving -1.916666667 + y = -2.381934322 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + y = -2.381934322 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + y = -2.381934322 + 1.916666667 y = -2.381934322 + 1.916666667 Combine like terms: -2.381934322 + 1.916666667 = -0.465267655 y = -0.465267655 Simplifying y = -0.465267655Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.298600989, -0.465267655}Solution
y = {4.298600989, -0.465267655}
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