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Simplifying -3(-4 + -6y) * 7(-1y + 5) = -8 Reorder the terms: -3(-4 + -6y) * 7(5 + -1y) = -8 Reorder the terms for easier multiplication: -3 * 7(-4 + -6y)(5 + -1y) = -8 Multiply -3 * 7 -21(-4 + -6y)(5 + -1y) = -8 Multiply (-4 + -6y) * (5 + -1y) -21(-4(5 + -1y) + -6y * (5 + -1y)) = -8 -21((5 * -4 + -1y * -4) + -6y * (5 + -1y)) = -8 -21((-20 + 4y) + -6y * (5 + -1y)) = -8 -21(-20 + 4y + (5 * -6y + -1y * -6y)) = -8 -21(-20 + 4y + (-30y + 6y2)) = -8 Combine like terms: 4y + -30y = -26y -21(-20 + -26y + 6y2) = -8 (-20 * -21 + -26y * -21 + 6y2 * -21) = -8 (420 + 546y + -126y2) = -8 Solving 420 + 546y + -126y2 = -8 Solving for variable 'y'. Reorder the terms: 420 + 8 + 546y + -126y2 = -8 + 8 Combine like terms: 420 + 8 = 428 428 + 546y + -126y2 = -8 + 8 Combine like terms: -8 + 8 = 0 428 + 546y + -126y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(214 + 273y + -63y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(214 + 273y + -63y2)' equal to zero and attempt to solve: Simplifying 214 + 273y + -63y2 = 0 Solving 214 + 273y + -63y2 = 0 Begin completing the square. Divide all terms by -63 the coefficient of the squared term: Divide each side by '-63'. -3.396825397 + -4.333333333y + y2 = 0 Move the constant term to the right: Add '3.396825397' to each side of the equation. -3.396825397 + -4.333333333y + 3.396825397 + y2 = 0 + 3.396825397 Reorder the terms: -3.396825397 + 3.396825397 + -4.333333333y + y2 = 0 + 3.396825397 Combine like terms: -3.396825397 + 3.396825397 = 0.000000000 0.000000000 + -4.333333333y + y2 = 0 + 3.396825397 -4.333333333y + y2 = 0 + 3.396825397 Combine like terms: 0 + 3.396825397 = 3.396825397 -4.333333333y + y2 = 3.396825397 The y term is -4.333333333y. Take half its coefficient (-2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. -4.333333333y + 4.694444446 + y2 = 3.396825397 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333y + y2 = 3.396825397 + 4.694444446 Combine like terms: 3.396825397 + 4.694444446 = 8.091269843 4.694444446 + -4.333333333y + y2 = 8.091269843 Factor a perfect square on the left side: (y + -2.166666667)(y + -2.166666667) = 8.091269843 Calculate the square root of the right side: 2.844515748 Break this problem into two subproblems by setting (y + -2.166666667) equal to 2.844515748 and -2.844515748.Subproblem 1
y + -2.166666667 = 2.844515748 Simplifying y + -2.166666667 = 2.844515748 Reorder the terms: -2.166666667 + y = 2.844515748 Solving -2.166666667 + y = 2.844515748 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + y = 2.844515748 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + y = 2.844515748 + 2.166666667 y = 2.844515748 + 2.166666667 Combine like terms: 2.844515748 + 2.166666667 = 5.011182415 y = 5.011182415 Simplifying y = 5.011182415Subproblem 2
y + -2.166666667 = -2.844515748 Simplifying y + -2.166666667 = -2.844515748 Reorder the terms: -2.166666667 + y = -2.844515748 Solving -2.166666667 + y = -2.844515748 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + y = -2.844515748 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + y = -2.844515748 + 2.166666667 y = -2.844515748 + 2.166666667 Combine like terms: -2.844515748 + 2.166666667 = -0.677849081 y = -0.677849081 Simplifying y = -0.677849081Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.011182415, -0.677849081}Solution
y = {5.011182415, -0.677849081}
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