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Simplifying 3y + 7(2y + -4) * y = 12 Reorder the terms: 3y + 7(-4 + 2y) * y = 12 Reorder the terms for easier multiplication: 3y + 7y(-4 + 2y) = 12 3y + (-4 * 7y + 2y * 7y) = 12 3y + (-28y + 14y2) = 12 Combine like terms: 3y + -28y = -25y -25y + 14y2 = 12 Solving -25y + 14y2 = 12 Solving for variable 'y'. Reorder the terms: -12 + -25y + 14y2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -25y + 14y2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.8571428571 + -1.785714286y + y2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -1.785714286y + 0.8571428571 + y2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -1.785714286y + y2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -1.785714286y + y2 = 0 + 0.8571428571 -1.785714286y + y2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -1.785714286y + y2 = 0.8571428571 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 = 0.8571428571 + 0.7971938778 Reorder the terms: 0.7971938778 + -1.785714286y + y2 = 0.8571428571 + 0.7971938778 Combine like terms: 0.8571428571 + 0.7971938778 = 1.6543367349 0.7971938778 + -1.785714286y + y2 = 1.6543367349 Factor a perfect square on the left side: (y + -0.892857143)(y + -0.892857143) = 1.6543367349 Calculate the square root of the right side: 1.286210222 Break this problem into two subproblems by setting (y + -0.892857143) equal to 1.286210222 and -1.286210222.Subproblem 1
y + -0.892857143 = 1.286210222 Simplifying y + -0.892857143 = 1.286210222 Reorder the terms: -0.892857143 + y = 1.286210222 Solving -0.892857143 + y = 1.286210222 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 = 1.286210222 + 0.892857143 Combine like terms: -0.892857143 + 0.892857143 = 0.000000000 0.000000000 + y = 1.286210222 + 0.892857143 y = 1.286210222 + 0.892857143 Combine like terms: 1.286210222 + 0.892857143 = 2.179067365 y = 2.179067365 Simplifying y = 2.179067365Subproblem 2
y + -0.892857143 = -1.286210222 Simplifying y + -0.892857143 = -1.286210222 Reorder the terms: -0.892857143 + y = -1.286210222 Solving -0.892857143 + y = -1.286210222 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 = -1.286210222 + 0.892857143 Combine like terms: -0.892857143 + 0.892857143 = 0.000000000 0.000000000 + y = -1.286210222 + 0.892857143 y = -1.286210222 + 0.892857143 Combine like terms: -1.286210222 + 0.892857143 = -0.393353079 y = -0.393353079 Simplifying y = -0.393353079Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.179067365, -0.393353079}
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