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Simplifying 7y2 + y + -64 = 0 Reorder the terms: -64 + y + 7y2 = 0 Solving -64 + y + 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'. -9.142857143 + 0.1428571429y + y2 = 0 Move the constant term to the right: Add '9.142857143' to each side of the equation. -9.142857143 + 0.1428571429y + 9.142857143 + y2 = 0 + 9.142857143 Reorder the terms: -9.142857143 + 9.142857143 + 0.1428571429y + y2 = 0 + 9.142857143 Combine like terms: -9.142857143 + 9.142857143 = 0.000000000 0.000000000 + 0.1428571429y + y2 = 0 + 9.142857143 0.1428571429y + y2 = 0 + 9.142857143 Combine like terms: 0 + 9.142857143 = 9.142857143 0.1428571429y + y2 = 9.142857143 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1428571429y + 0.25 + y2 = 9.142857143 + 0.25 Reorder the terms: 0.25 + 0.1428571429y + y2 = 9.142857143 + 0.25 Combine like terms: 9.142857143 + 0.25 = 9.392857143 0.25 + 0.1428571429y + y2 = 9.392857143 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 9.392857143 Calculate the square root of the right side: 3.06477685 Break this problem into two subproblems by setting (y + 0.5) equal to 3.06477685 and -3.06477685.Subproblem 1
y + 0.5 = 3.06477685 Simplifying y + 0.5 = 3.06477685 Reorder the terms: 0.5 + y = 3.06477685 Solving 0.5 + y = 3.06477685 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 3.06477685 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 3.06477685 + -0.5 y = 3.06477685 + -0.5 Combine like terms: 3.06477685 + -0.5 = 2.56477685 y = 2.56477685 Simplifying y = 2.56477685Subproblem 2
y + 0.5 = -3.06477685 Simplifying y + 0.5 = -3.06477685 Reorder the terms: 0.5 + y = -3.06477685 Solving 0.5 + y = -3.06477685 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -3.06477685 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -3.06477685 + -0.5 y = -3.06477685 + -0.5 Combine like terms: -3.06477685 + -0.5 = -3.56477685 y = -3.56477685 Simplifying y = -3.56477685Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.56477685, -3.56477685}
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