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Simplifying 7y2 + -7y + -15 = 0 Reorder the terms: -15 + -7y + 7y2 = 0 Solving -15 + -7y + 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'. -2.142857143 + -1y + y2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + -1y + 2.142857143 + y2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + -1y + y2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + -1y + y2 = 0 + 2.142857143 -1y + y2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 -1y + y2 = 2.142857143 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 2.142857143 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 2.142857143 + 0.25 Combine like terms: 2.142857143 + 0.25 = 2.392857143 0.25 + -1y + y2 = 2.392857143 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 2.392857143 Calculate the square root of the right side: 1.546886273 Break this problem into two subproblems by setting (y + -0.5) equal to 1.546886273 and -1.546886273.Subproblem 1
y + -0.5 = 1.546886273 Simplifying y + -0.5 = 1.546886273 Reorder the terms: -0.5 + y = 1.546886273 Solving -0.5 + y = 1.546886273 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 1.546886273 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 1.546886273 + 0.5 y = 1.546886273 + 0.5 Combine like terms: 1.546886273 + 0.5 = 2.046886273 y = 2.046886273 Simplifying y = 2.046886273Subproblem 2
y + -0.5 = -1.546886273 Simplifying y + -0.5 = -1.546886273 Reorder the terms: -0.5 + y = -1.546886273 Solving -0.5 + y = -1.546886273 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -1.546886273 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -1.546886273 + 0.5 y = -1.546886273 + 0.5 Combine like terms: -1.546886273 + 0.5 = -1.046886273 y = -1.046886273 Simplifying y = -1.046886273Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.046886273, -1.046886273}
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