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Simplifying 7y2 + 10y + 10 = 74 Reorder the terms: 10 + 10y + 7y2 = 74 Solving 10 + 10y + 7y2 = 74 Solving for variable 'y'. Reorder the terms: 10 + -74 + 10y + 7y2 = 74 + -74 Combine like terms: 10 + -74 = -64 -64 + 10y + 7y2 = 74 + -74 Combine like terms: 74 + -74 = 0 -64 + 10y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -9.142857143 + 1.428571429y + y2 = 0 Move the constant term to the right: Add '9.142857143' to each side of the equation. -9.142857143 + 1.428571429y + 9.142857143 + y2 = 0 + 9.142857143 Reorder the terms: -9.142857143 + 9.142857143 + 1.428571429y + y2 = 0 + 9.142857143 Combine like terms: -9.142857143 + 9.142857143 = 0.000000000 0.000000000 + 1.428571429y + y2 = 0 + 9.142857143 1.428571429y + y2 = 0 + 9.142857143 Combine like terms: 0 + 9.142857143 = 9.142857143 1.428571429y + y2 = 9.142857143 The y term is 1.428571429y. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429y + 0.5102040819 + y2 = 9.142857143 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429y + y2 = 9.142857143 + 0.5102040819 Combine like terms: 9.142857143 + 0.5102040819 = 9.6530612249 0.5102040819 + 1.428571429y + y2 = 9.6530612249 Factor a perfect square on the left side: (y + 0.7142857145)(y + 0.7142857145) = 9.6530612249 Calculate the square root of the right side: 3.106937596 Break this problem into two subproblems by setting (y + 0.7142857145) equal to 3.106937596 and -3.106937596.Subproblem 1
y + 0.7142857145 = 3.106937596 Simplifying y + 0.7142857145 = 3.106937596 Reorder the terms: 0.7142857145 + y = 3.106937596 Solving 0.7142857145 + y = 3.106937596 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + y = 3.106937596 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + y = 3.106937596 + -0.7142857145 y = 3.106937596 + -0.7142857145 Combine like terms: 3.106937596 + -0.7142857145 = 2.3926518815 y = 2.3926518815 Simplifying y = 2.3926518815Subproblem 2
y + 0.7142857145 = -3.106937596 Simplifying y + 0.7142857145 = -3.106937596 Reorder the terms: 0.7142857145 + y = -3.106937596 Solving 0.7142857145 + y = -3.106937596 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + y = -3.106937596 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + y = -3.106937596 + -0.7142857145 y = -3.106937596 + -0.7142857145 Combine like terms: -3.106937596 + -0.7142857145 = -3.8212233105 y = -3.8212233105 Simplifying y = -3.8212233105Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.3926518815, -3.8212233105}
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