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Simplifying -1(3y + 3)(-2y + -5) = 1 Reorder the terms: -1(3 + 3y)(-2y + -5) = 1 Reorder the terms: -1(3 + 3y)(-5 + -2y) = 1 Multiply (3 + 3y) * (-5 + -2y) -1(3(-5 + -2y) + 3y * (-5 + -2y)) = 1 -1((-5 * 3 + -2y * 3) + 3y * (-5 + -2y)) = 1 -1((-15 + -6y) + 3y * (-5 + -2y)) = 1 -1(-15 + -6y + (-5 * 3y + -2y * 3y)) = 1 -1(-15 + -6y + (-15y + -6y2)) = 1 Combine like terms: -6y + -15y = -21y -1(-15 + -21y + -6y2) = 1 (-15 * -1 + -21y * -1 + -6y2 * -1) = 1 (15 + 21y + 6y2) = 1 Solving 15 + 21y + 6y2 = 1 Solving for variable 'y'. Reorder the terms: 15 + -1 + 21y + 6y2 = 1 + -1 Combine like terms: 15 + -1 = 14 14 + 21y + 6y2 = 1 + -1 Combine like terms: 1 + -1 = 0 14 + 21y + 6y2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.333333333 + 3.5y + y2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + 3.5y + -2.333333333 + y2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + 3.5y + y2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + 3.5y + y2 = 0 + -2.333333333 3.5y + y2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 3.5y + y2 = -2.333333333 The y term is 3.5y. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5y + 3.0625 + y2 = -2.333333333 + 3.0625 Reorder the terms: 3.0625 + 3.5y + y2 = -2.333333333 + 3.0625 Combine like terms: -2.333333333 + 3.0625 = 0.729166667 3.0625 + 3.5y + y2 = 0.729166667 Factor a perfect square on the left side: (y + 1.75)(y + 1.75) = 0.729166667 Calculate the square root of the right side: 0.853912564 Break this problem into two subproblems by setting (y + 1.75) equal to 0.853912564 and -0.853912564.Subproblem 1
y + 1.75 = 0.853912564 Simplifying y + 1.75 = 0.853912564 Reorder the terms: 1.75 + y = 0.853912564 Solving 1.75 + y = 0.853912564 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = 0.853912564 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = 0.853912564 + -1.75 y = 0.853912564 + -1.75 Combine like terms: 0.853912564 + -1.75 = -0.896087436 y = -0.896087436 Simplifying y = -0.896087436Subproblem 2
y + 1.75 = -0.853912564 Simplifying y + 1.75 = -0.853912564 Reorder the terms: 1.75 + y = -0.853912564 Solving 1.75 + y = -0.853912564 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = -0.853912564 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = -0.853912564 + -1.75 y = -0.853912564 + -1.75 Combine like terms: -0.853912564 + -1.75 = -2.603912564 y = -2.603912564 Simplifying y = -2.603912564Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.896087436, -2.603912564}
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