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Simplifying 7y2 + 9y + 1 = 0 Reorder the terms: 1 + 9y + 7y2 = 0 Solving 1 + 9y + 7y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 1.285714286y + y2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 1.285714286y + -0.1428571429 + y2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 1.285714286y + y2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 1.285714286y + y2 = 0 + -0.1428571429 1.285714286y + y2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 1.285714286y + y2 = -0.1428571429 The y term is 1.285714286y. Take half its coefficient (0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. 1.285714286y + 0.4132653063 + y2 = -0.1428571429 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286y + y2 = -0.1428571429 + 0.4132653063 Combine like terms: -0.1428571429 + 0.4132653063 = 0.2704081634 0.4132653063 + 1.285714286y + y2 = 0.2704081634 Factor a perfect square on the left side: (y + 0.642857143)(y + 0.642857143) = 0.2704081634 Calculate the square root of the right side: 0.520007849 Break this problem into two subproblems by setting (y + 0.642857143) equal to 0.520007849 and -0.520007849.Subproblem 1
y + 0.642857143 = 0.520007849 Simplifying y + 0.642857143 = 0.520007849 Reorder the terms: 0.642857143 + y = 0.520007849 Solving 0.642857143 + y = 0.520007849 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + y = 0.520007849 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + y = 0.520007849 + -0.642857143 y = 0.520007849 + -0.642857143 Combine like terms: 0.520007849 + -0.642857143 = -0.122849294 y = -0.122849294 Simplifying y = -0.122849294Subproblem 2
y + 0.642857143 = -0.520007849 Simplifying y + 0.642857143 = -0.520007849 Reorder the terms: 0.642857143 + y = -0.520007849 Solving 0.642857143 + y = -0.520007849 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + y = -0.520007849 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + y = -0.520007849 + -0.642857143 y = -0.520007849 + -0.642857143 Combine like terms: -0.520007849 + -0.642857143 = -1.162864992 y = -1.162864992 Simplifying y = -1.162864992Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.122849294, -1.162864992}
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