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Simplifying 7y2 + -16y + -20 = 0 Reorder the terms: -20 + -16y + 7y2 = 0 Solving -20 + -16y + 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'. -2.857142857 + -2.285714286y + y2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + -2.285714286y + 2.857142857 + y2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + -2.285714286y + y2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + -2.285714286y + y2 = 0 + 2.857142857 -2.285714286y + y2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 -2.285714286y + y2 = 2.857142857 The y term is -2.285714286y. Take half its coefficient (-1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. -2.285714286y + 1.306122449 + y2 = 2.857142857 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286y + y2 = 2.857142857 + 1.306122449 Combine like terms: 2.857142857 + 1.306122449 = 4.163265306 1.306122449 + -2.285714286y + y2 = 4.163265306 Factor a perfect square on the left side: (y + -1.142857143)(y + -1.142857143) = 4.163265306 Calculate the square root of the right side: 2.040408122 Break this problem into two subproblems by setting (y + -1.142857143) equal to 2.040408122 and -2.040408122.Subproblem 1
y + -1.142857143 = 2.040408122 Simplifying y + -1.142857143 = 2.040408122 Reorder the terms: -1.142857143 + y = 2.040408122 Solving -1.142857143 + y = 2.040408122 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + y = 2.040408122 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + y = 2.040408122 + 1.142857143 y = 2.040408122 + 1.142857143 Combine like terms: 2.040408122 + 1.142857143 = 3.183265265 y = 3.183265265 Simplifying y = 3.183265265Subproblem 2
y + -1.142857143 = -2.040408122 Simplifying y + -1.142857143 = -2.040408122 Reorder the terms: -1.142857143 + y = -2.040408122 Solving -1.142857143 + y = -2.040408122 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + y = -2.040408122 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + y = -2.040408122 + 1.142857143 y = -2.040408122 + 1.142857143 Combine like terms: -2.040408122 + 1.142857143 = -0.897550979 y = -0.897550979 Simplifying y = -0.897550979Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.183265265, -0.897550979}
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