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Simplifying 7y2 + -16y + -24 = 0 Reorder the terms: -24 + -16y + 7y2 = 0 Solving -24 + -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'. -3.428571429 + -2.285714286y + y2 = 0 Move the constant term to the right: Add '3.428571429' to each side of the equation. -3.428571429 + -2.285714286y + 3.428571429 + y2 = 0 + 3.428571429 Reorder the terms: -3.428571429 + 3.428571429 + -2.285714286y + y2 = 0 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + -2.285714286y + y2 = 0 + 3.428571429 -2.285714286y + y2 = 0 + 3.428571429 Combine like terms: 0 + 3.428571429 = 3.428571429 -2.285714286y + y2 = 3.428571429 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 = 3.428571429 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286y + y2 = 3.428571429 + 1.306122449 Combine like terms: 3.428571429 + 1.306122449 = 4.734693878 1.306122449 + -2.285714286y + y2 = 4.734693878 Factor a perfect square on the left side: (y + -1.142857143)(y + -1.142857143) = 4.734693878 Calculate the square root of the right side: 2.175935173 Break this problem into two subproblems by setting (y + -1.142857143) equal to 2.175935173 and -2.175935173.Subproblem 1
y + -1.142857143 = 2.175935173 Simplifying y + -1.142857143 = 2.175935173 Reorder the terms: -1.142857143 + y = 2.175935173 Solving -1.142857143 + y = 2.175935173 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 = 2.175935173 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + y = 2.175935173 + 1.142857143 y = 2.175935173 + 1.142857143 Combine like terms: 2.175935173 + 1.142857143 = 3.318792316 y = 3.318792316 Simplifying y = 3.318792316Subproblem 2
y + -1.142857143 = -2.175935173 Simplifying y + -1.142857143 = -2.175935173 Reorder the terms: -1.142857143 + y = -2.175935173 Solving -1.142857143 + y = -2.175935173 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 = -2.175935173 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + y = -2.175935173 + 1.142857143 y = -2.175935173 + 1.142857143 Combine like terms: -2.175935173 + 1.142857143 = -1.03307803 y = -1.03307803 Simplifying y = -1.03307803Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.318792316, -1.03307803}
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