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Simplifying -7y2 + -4y + 5 = 0 Reorder the terms: 5 + -4y + -7y2 = 0 Solving 5 + -4y + -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'. -0.7142857143 + 0.5714285714y + y2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 0.5714285714y + 0.7142857143 + y2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 0.5714285714y + y2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 0.5714285714y + y2 = 0 + 0.7142857143 0.5714285714y + y2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 0.5714285714y + y2 = 0.7142857143 The y term is 0.5714285714y. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714y + 0.08163265305 + y2 = 0.7142857143 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714y + y2 = 0.7142857143 + 0.08163265305 Combine like terms: 0.7142857143 + 0.08163265305 = 0.79591836735 0.08163265305 + 0.5714285714y + y2 = 0.79591836735 Factor a perfect square on the left side: (y + 0.2857142857)(y + 0.2857142857) = 0.79591836735 Calculate the square root of the right side: 0.892142571 Break this problem into two subproblems by setting (y + 0.2857142857) equal to 0.892142571 and -0.892142571.Subproblem 1
y + 0.2857142857 = 0.892142571 Simplifying y + 0.2857142857 = 0.892142571 Reorder the terms: 0.2857142857 + y = 0.892142571 Solving 0.2857142857 + y = 0.892142571 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + y = 0.892142571 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + y = 0.892142571 + -0.2857142857 y = 0.892142571 + -0.2857142857 Combine like terms: 0.892142571 + -0.2857142857 = 0.6064282853 y = 0.6064282853 Simplifying y = 0.6064282853Subproblem 2
y + 0.2857142857 = -0.892142571 Simplifying y + 0.2857142857 = -0.892142571 Reorder the terms: 0.2857142857 + y = -0.892142571 Solving 0.2857142857 + y = -0.892142571 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + y = -0.892142571 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + y = -0.892142571 + -0.2857142857 y = -0.892142571 + -0.2857142857 Combine like terms: -0.892142571 + -0.2857142857 = -1.1778568567 y = -1.1778568567 Simplifying y = -1.1778568567Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.6064282853, -1.1778568567}
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