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Simplifying 7y2 + -16y + -28 = 0 Reorder the terms: -28 + -16y + 7y2 = 0 Solving -28 + -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'. -4 + -2.285714286y + y2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -2.285714286y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + -2.285714286y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2.285714286y + y2 = 0 + 4 -2.285714286y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2.285714286y + y2 = 4 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 = 4 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286y + y2 = 4 + 1.306122449 Combine like terms: 4 + 1.306122449 = 5.306122449 1.306122449 + -2.285714286y + y2 = 5.306122449 Factor a perfect square on the left side: (y + -1.142857143)(y + -1.142857143) = 5.306122449 Calculate the square root of the right side: 2.303502214 Break this problem into two subproblems by setting (y + -1.142857143) equal to 2.303502214 and -2.303502214.Subproblem 1
y + -1.142857143 = 2.303502214 Simplifying y + -1.142857143 = 2.303502214 Reorder the terms: -1.142857143 + y = 2.303502214 Solving -1.142857143 + y = 2.303502214 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 = 2.303502214 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + y = 2.303502214 + 1.142857143 y = 2.303502214 + 1.142857143 Combine like terms: 2.303502214 + 1.142857143 = 3.446359357 y = 3.446359357 Simplifying y = 3.446359357Subproblem 2
y + -1.142857143 = -2.303502214 Simplifying y + -1.142857143 = -2.303502214 Reorder the terms: -1.142857143 + y = -2.303502214 Solving -1.142857143 + y = -2.303502214 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 = -2.303502214 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + y = -2.303502214 + 1.142857143 y = -2.303502214 + 1.142857143 Combine like terms: -2.303502214 + 1.142857143 = -1.160645071 y = -1.160645071 Simplifying y = -1.160645071Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.446359357, -1.160645071}
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