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Simplifying 2y2 + y + -1(1 + 2y) = 13 2y2 + y + (1 * -1 + 2y * -1) = 13 2y2 + y + (-1 + -2y) = 13 Reorder the terms: -1 + y + -2y + 2y2 = 13 Combine like terms: y + -2y = -1y -1 + -1y + 2y2 = 13 Solving -1 + -1y + 2y2 = 13 Solving for variable 'y'. Reorder the terms: -1 + -13 + -1y + 2y2 = 13 + -13 Combine like terms: -1 + -13 = -14 -14 + -1y + 2y2 = 13 + -13 Combine like terms: 13 + -13 = 0 -14 + -1y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7 + -0.5y + y2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -0.5y + 7 + y2 = 0 + 7 Reorder the terms: -7 + 7 + -0.5y + y2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -0.5y + y2 = 0 + 7 -0.5y + y2 = 0 + 7 Combine like terms: 0 + 7 = 7 -0.5y + y2 = 7 The y term is -0.5y. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5y + 0.0625 + y2 = 7 + 0.0625 Reorder the terms: 0.0625 + -0.5y + y2 = 7 + 0.0625 Combine like terms: 7 + 0.0625 = 7.0625 0.0625 + -0.5y + y2 = 7.0625 Factor a perfect square on the left side: (y + -0.25)(y + -0.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (y + -0.25) equal to 2.657536453 and -2.657536453.Subproblem 1
y + -0.25 = 2.657536453 Simplifying y + -0.25 = 2.657536453 Reorder the terms: -0.25 + y = 2.657536453 Solving -0.25 + y = 2.657536453 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + y = 2.657536453 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + y = 2.657536453 + 0.25 y = 2.657536453 + 0.25 Combine like terms: 2.657536453 + 0.25 = 2.907536453 y = 2.907536453 Simplifying y = 2.907536453Subproblem 2
y + -0.25 = -2.657536453 Simplifying y + -0.25 = -2.657536453 Reorder the terms: -0.25 + y = -2.657536453 Solving -0.25 + y = -2.657536453 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + y = -2.657536453 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + y = -2.657536453 + 0.25 y = -2.657536453 + 0.25 Combine like terms: -2.657536453 + 0.25 = -2.407536453 y = -2.407536453 Simplifying y = -2.407536453Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.907536453, -2.407536453}
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