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Simplifying 7y(4 + -2y) = 3(y + -3) (4 * 7y + -2y * 7y) = 3(y + -3) (28y + -14y2) = 3(y + -3) Reorder the terms: 28y + -14y2 = 3(-3 + y) 28y + -14y2 = (-3 * 3 + y * 3) 28y + -14y2 = (-9 + 3y) Solving 28y + -14y2 = -9 + 3y Solving for variable 'y'. Reorder the terms: 9 + 28y + -3y + -14y2 = -9 + 3y + 9 + -3y Combine like terms: 28y + -3y = 25y 9 + 25y + -14y2 = -9 + 3y + 9 + -3y Reorder the terms: 9 + 25y + -14y2 = -9 + 9 + 3y + -3y Combine like terms: -9 + 9 = 0 9 + 25y + -14y2 = 0 + 3y + -3y 9 + 25y + -14y2 = 3y + -3y Combine like terms: 3y + -3y = 0 9 + 25y + -14y2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -0.6428571429 + -1.785714286y + y2 = 0 Move the constant term to the right: Add '0.6428571429' to each side of the equation. -0.6428571429 + -1.785714286y + 0.6428571429 + y2 = 0 + 0.6428571429 Reorder the terms: -0.6428571429 + 0.6428571429 + -1.785714286y + y2 = 0 + 0.6428571429 Combine like terms: -0.6428571429 + 0.6428571429 = 0.0000000000 0.0000000000 + -1.785714286y + y2 = 0 + 0.6428571429 -1.785714286y + y2 = 0 + 0.6428571429 Combine like terms: 0 + 0.6428571429 = 0.6428571429 -1.785714286y + y2 = 0.6428571429 The y term is -1.785714286y. Take half its coefficient (-0.892857143). Square it (0.7971938778) and add it to both sides. Add '0.7971938778' to each side of the equation. -1.785714286y + 0.7971938778 + y2 = 0.6428571429 + 0.7971938778 Reorder the terms: 0.7971938778 + -1.785714286y + y2 = 0.6428571429 + 0.7971938778 Combine like terms: 0.6428571429 + 0.7971938778 = 1.4400510207 0.7971938778 + -1.785714286y + y2 = 1.4400510207 Factor a perfect square on the left side: (y + -0.892857143)(y + -0.892857143) = 1.4400510207 Calculate the square root of the right side: 1.200021258 Break this problem into two subproblems by setting (y + -0.892857143) equal to 1.200021258 and -1.200021258.Subproblem 1
y + -0.892857143 = 1.200021258 Simplifying y + -0.892857143 = 1.200021258 Reorder the terms: -0.892857143 + y = 1.200021258 Solving -0.892857143 + y = 1.200021258 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.892857143' to each side of the equation. -0.892857143 + 0.892857143 + y = 1.200021258 + 0.892857143 Combine like terms: -0.892857143 + 0.892857143 = 0.000000000 0.000000000 + y = 1.200021258 + 0.892857143 y = 1.200021258 + 0.892857143 Combine like terms: 1.200021258 + 0.892857143 = 2.092878401 y = 2.092878401 Simplifying y = 2.092878401Subproblem 2
y + -0.892857143 = -1.200021258 Simplifying y + -0.892857143 = -1.200021258 Reorder the terms: -0.892857143 + y = -1.200021258 Solving -0.892857143 + y = -1.200021258 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.892857143' to each side of the equation. -0.892857143 + 0.892857143 + y = -1.200021258 + 0.892857143 Combine like terms: -0.892857143 + 0.892857143 = 0.000000000 0.000000000 + y = -1.200021258 + 0.892857143 y = -1.200021258 + 0.892857143 Combine like terms: -1.200021258 + 0.892857143 = -0.307164115 y = -0.307164115 Simplifying y = -0.307164115Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.092878401, -0.307164115}
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