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Simplifying 7y2 + 14y + -5 = 0 Reorder the terms: -5 + 14y + 7y2 = 0 Solving -5 + 14y + 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 + 2y + y2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 2y + 0.7142857143 + y2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 2y + y2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 2y + y2 = 0 + 0.7142857143 2y + y2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 2y + y2 = 0.7142857143 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 0.7142857143 + 1 Reorder the terms: 1 + 2y + y2 = 0.7142857143 + 1 Combine like terms: 0.7142857143 + 1 = 1.7142857143 1 + 2y + y2 = 1.7142857143 Factor a perfect square on the left side: (y + 1)(y + 1) = 1.7142857143 Calculate the square root of the right side: 1.309307341 Break this problem into two subproblems by setting (y + 1) equal to 1.309307341 and -1.309307341.Subproblem 1
y + 1 = 1.309307341 Simplifying y + 1 = 1.309307341 Reorder the terms: 1 + y = 1.309307341 Solving 1 + y = 1.309307341 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 1.309307341 + -1 Combine like terms: 1 + -1 = 0 0 + y = 1.309307341 + -1 y = 1.309307341 + -1 Combine like terms: 1.309307341 + -1 = 0.309307341 y = 0.309307341 Simplifying y = 0.309307341Subproblem 2
y + 1 = -1.309307341 Simplifying y + 1 = -1.309307341 Reorder the terms: 1 + y = -1.309307341 Solving 1 + y = -1.309307341 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -1.309307341 + -1 Combine like terms: 1 + -1 = 0 0 + y = -1.309307341 + -1 y = -1.309307341 + -1 Combine like terms: -1.309307341 + -1 = -2.309307341 y = -2.309307341 Simplifying y = -2.309307341Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.309307341, -2.309307341}
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