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Simplifying -2y(6y + -3) + -1y = 2(y + -4) Reorder the terms: -2y(-3 + 6y) + -1y = 2(y + -4) (-3 * -2y + 6y * -2y) + -1y = 2(y + -4) (6y + -12y2) + -1y = 2(y + -4) Reorder the terms: 6y + -1y + -12y2 = 2(y + -4) Combine like terms: 6y + -1y = 5y 5y + -12y2 = 2(y + -4) Reorder the terms: 5y + -12y2 = 2(-4 + y) 5y + -12y2 = (-4 * 2 + y * 2) 5y + -12y2 = (-8 + 2y) Solving 5y + -12y2 = -8 + 2y Solving for variable 'y'. Reorder the terms: 8 + 5y + -2y + -12y2 = -8 + 2y + 8 + -2y Combine like terms: 5y + -2y = 3y 8 + 3y + -12y2 = -8 + 2y + 8 + -2y Reorder the terms: 8 + 3y + -12y2 = -8 + 8 + 2y + -2y Combine like terms: -8 + 8 = 0 8 + 3y + -12y2 = 0 + 2y + -2y 8 + 3y + -12y2 = 2y + -2y Combine like terms: 2y + -2y = 0 8 + 3y + -12y2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.6666666667 + -0.25y + y2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -0.25y + 0.6666666667 + y2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -0.25y + y2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -0.25y + y2 = 0 + 0.6666666667 -0.25y + y2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -0.25y + y2 = 0.6666666667 The y term is -0.25y. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25y + 0.015625 + y2 = 0.6666666667 + 0.015625 Reorder the terms: 0.015625 + -0.25y + y2 = 0.6666666667 + 0.015625 Combine like terms: 0.6666666667 + 0.015625 = 0.6822916667 0.015625 + -0.25y + y2 = 0.6822916667 Factor a perfect square on the left side: (y + -0.125)(y + -0.125) = 0.6822916667 Calculate the square root of the right side: 0.826009483 Break this problem into two subproblems by setting (y + -0.125) equal to 0.826009483 and -0.826009483.Subproblem 1
y + -0.125 = 0.826009483 Simplifying y + -0.125 = 0.826009483 Reorder the terms: -0.125 + y = 0.826009483 Solving -0.125 + y = 0.826009483 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + y = 0.826009483 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + y = 0.826009483 + 0.125 y = 0.826009483 + 0.125 Combine like terms: 0.826009483 + 0.125 = 0.951009483 y = 0.951009483 Simplifying y = 0.951009483Subproblem 2
y + -0.125 = -0.826009483 Simplifying y + -0.125 = -0.826009483 Reorder the terms: -0.125 + y = -0.826009483 Solving -0.125 + y = -0.826009483 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + y = -0.826009483 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + y = -0.826009483 + 0.125 y = -0.826009483 + 0.125 Combine like terms: -0.826009483 + 0.125 = -0.701009483 y = -0.701009483 Simplifying y = -0.701009483Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.951009483, -0.701009483}
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