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Simplifying (7y + 6)(5y + -4) = 94 Reorder the terms: (6 + 7y)(5y + -4) = 94 Reorder the terms: (6 + 7y)(-4 + 5y) = 94 Multiply (6 + 7y) * (-4 + 5y) (6(-4 + 5y) + 7y * (-4 + 5y)) = 94 ((-4 * 6 + 5y * 6) + 7y * (-4 + 5y)) = 94 ((-24 + 30y) + 7y * (-4 + 5y)) = 94 (-24 + 30y + (-4 * 7y + 5y * 7y)) = 94 (-24 + 30y + (-28y + 35y2)) = 94 Combine like terms: 30y + -28y = 2y (-24 + 2y + 35y2) = 94 Solving -24 + 2y + 35y2 = 94 Solving for variable 'y'. Reorder the terms: -24 + -94 + 2y + 35y2 = 94 + -94 Combine like terms: -24 + -94 = -118 -118 + 2y + 35y2 = 94 + -94 Combine like terms: 94 + -94 = 0 -118 + 2y + 35y2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -3.371428571 + 0.05714285714y + y2 = 0 Move the constant term to the right: Add '3.371428571' to each side of the equation. -3.371428571 + 0.05714285714y + 3.371428571 + y2 = 0 + 3.371428571 Reorder the terms: -3.371428571 + 3.371428571 + 0.05714285714y + y2 = 0 + 3.371428571 Combine like terms: -3.371428571 + 3.371428571 = 0.000000000 0.000000000 + 0.05714285714y + y2 = 0 + 3.371428571 0.05714285714y + y2 = 0 + 3.371428571 Combine like terms: 0 + 3.371428571 = 3.371428571 0.05714285714y + y2 = 3.371428571 The y term is 0.05714285714y. Take half its coefficient (0.02857142857). Square it (0.0008163265305) and add it to both sides. Add '0.0008163265305' to each side of the equation. 0.05714285714y + 0.0008163265305 + y2 = 3.371428571 + 0.0008163265305 Reorder the terms: 0.0008163265305 + 0.05714285714y + y2 = 3.371428571 + 0.0008163265305 Combine like terms: 3.371428571 + 0.0008163265305 = 3.3722448975305 0.0008163265305 + 0.05714285714y + y2 = 3.3722448975305 Factor a perfect square on the left side: (y + 0.02857142857)(y + 0.02857142857) = 3.3722448975305 Calculate the square root of the right side: 1.83636731 Break this problem into two subproblems by setting (y + 0.02857142857) equal to 1.83636731 and -1.83636731.Subproblem 1
y + 0.02857142857 = 1.83636731 Simplifying y + 0.02857142857 = 1.83636731 Reorder the terms: 0.02857142857 + y = 1.83636731 Solving 0.02857142857 + y = 1.83636731 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.02857142857' to each side of the equation. 0.02857142857 + -0.02857142857 + y = 1.83636731 + -0.02857142857 Combine like terms: 0.02857142857 + -0.02857142857 = 0.00000000000 0.00000000000 + y = 1.83636731 + -0.02857142857 y = 1.83636731 + -0.02857142857 Combine like terms: 1.83636731 + -0.02857142857 = 1.80779588143 y = 1.80779588143 Simplifying y = 1.80779588143Subproblem 2
y + 0.02857142857 = -1.83636731 Simplifying y + 0.02857142857 = -1.83636731 Reorder the terms: 0.02857142857 + y = -1.83636731 Solving 0.02857142857 + y = -1.83636731 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.02857142857' to each side of the equation. 0.02857142857 + -0.02857142857 + y = -1.83636731 + -0.02857142857 Combine like terms: 0.02857142857 + -0.02857142857 = 0.00000000000 0.00000000000 + y = -1.83636731 + -0.02857142857 y = -1.83636731 + -0.02857142857 Combine like terms: -1.83636731 + -0.02857142857 = -1.86493873857 y = -1.86493873857 Simplifying y = -1.86493873857Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.80779588143, -1.86493873857}
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