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Simplifying 2y2 + 7y + -10 = 0 Reorder the terms: -10 + 7y + 2y2 = 0 Solving -10 + 7y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + 3.5y + y2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 3.5y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + 3.5y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3.5y + y2 = 0 + 5 3.5y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 3.5y + y2 = 5 The y term is 3.5y. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5y + 3.0625 + y2 = 5 + 3.0625 Reorder the terms: 3.0625 + 3.5y + y2 = 5 + 3.0625 Combine like terms: 5 + 3.0625 = 8.0625 3.0625 + 3.5y + y2 = 8.0625 Factor a perfect square on the left side: (y + 1.75)(y + 1.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (y + 1.75) equal to 2.839454173 and -2.839454173.Subproblem 1
y + 1.75 = 2.839454173 Simplifying y + 1.75 = 2.839454173 Reorder the terms: 1.75 + y = 2.839454173 Solving 1.75 + y = 2.839454173 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = 2.839454173 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = 2.839454173 + -1.75 y = 2.839454173 + -1.75 Combine like terms: 2.839454173 + -1.75 = 1.089454173 y = 1.089454173 Simplifying y = 1.089454173Subproblem 2
y + 1.75 = -2.839454173 Simplifying y + 1.75 = -2.839454173 Reorder the terms: 1.75 + y = -2.839454173 Solving 1.75 + y = -2.839454173 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = -2.839454173 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = -2.839454173 + -1.75 y = -2.839454173 + -1.75 Combine like terms: -2.839454173 + -1.75 = -4.589454173 y = -4.589454173 Simplifying y = -4.589454173Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.089454173, -4.589454173}
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