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Simplifying 4y2 + 8y + -135 = 0 Reorder the terms: -135 + 8y + 4y2 = 0 Solving -135 + 8y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -33.75 + 2y + y2 = 0 Move the constant term to the right: Add '33.75' to each side of the equation. -33.75 + 2y + 33.75 + y2 = 0 + 33.75 Reorder the terms: -33.75 + 33.75 + 2y + y2 = 0 + 33.75 Combine like terms: -33.75 + 33.75 = 0.00 0.00 + 2y + y2 = 0 + 33.75 2y + y2 = 0 + 33.75 Combine like terms: 0 + 33.75 = 33.75 2y + y2 = 33.75 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 33.75 + 1 Reorder the terms: 1 + 2y + y2 = 33.75 + 1 Combine like terms: 33.75 + 1 = 34.75 1 + 2y + y2 = 34.75 Factor a perfect square on the left side: (y + 1)(y + 1) = 34.75 Calculate the square root of the right side: 5.894913061 Break this problem into two subproblems by setting (y + 1) equal to 5.894913061 and -5.894913061.Subproblem 1
y + 1 = 5.894913061 Simplifying y + 1 = 5.894913061 Reorder the terms: 1 + y = 5.894913061 Solving 1 + y = 5.894913061 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 5.894913061 + -1 Combine like terms: 1 + -1 = 0 0 + y = 5.894913061 + -1 y = 5.894913061 + -1 Combine like terms: 5.894913061 + -1 = 4.894913061 y = 4.894913061 Simplifying y = 4.894913061Subproblem 2
y + 1 = -5.894913061 Simplifying y + 1 = -5.894913061 Reorder the terms: 1 + y = -5.894913061 Solving 1 + y = -5.894913061 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -5.894913061 + -1 Combine like terms: 1 + -1 = 0 0 + y = -5.894913061 + -1 y = -5.894913061 + -1 Combine like terms: -5.894913061 + -1 = -6.894913061 y = -6.894913061 Simplifying y = -6.894913061Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.894913061, -6.894913061}
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