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Simplifying (5y + -3) + (4y + 9) * y = 0 Reorder the terms: (-3 + 5y) + (4y + 9) * y = 0 Remove parenthesis around (-3 + 5y) -3 + 5y + (4y + 9) * y = 0 Reorder the terms: -3 + 5y + (9 + 4y) * y = 0 Reorder the terms for easier multiplication: -3 + 5y + y(9 + 4y) = 0 -3 + 5y + (9 * y + 4y * y) = 0 -3 + 5y + (9y + 4y2) = 0 Combine like terms: 5y + 9y = 14y -3 + 14y + 4y2 = 0 Solving -3 + 14y + 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'. -0.75 + 3.5y + y2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 3.5y + 0.75 + y2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 3.5y + y2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 3.5y + y2 = 0 + 0.75 3.5y + y2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 3.5y + y2 = 0.75 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 = 0.75 + 3.0625 Reorder the terms: 3.0625 + 3.5y + y2 = 0.75 + 3.0625 Combine like terms: 0.75 + 3.0625 = 3.8125 3.0625 + 3.5y + y2 = 3.8125 Factor a perfect square on the left side: (y + 1.75)(y + 1.75) = 3.8125 Calculate the square root of the right side: 1.952562419 Break this problem into two subproblems by setting (y + 1.75) equal to 1.952562419 and -1.952562419.Subproblem 1
y + 1.75 = 1.952562419 Simplifying y + 1.75 = 1.952562419 Reorder the terms: 1.75 + y = 1.952562419 Solving 1.75 + y = 1.952562419 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 = 1.952562419 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = 1.952562419 + -1.75 y = 1.952562419 + -1.75 Combine like terms: 1.952562419 + -1.75 = 0.202562419 y = 0.202562419 Simplifying y = 0.202562419Subproblem 2
y + 1.75 = -1.952562419 Simplifying y + 1.75 = -1.952562419 Reorder the terms: 1.75 + y = -1.952562419 Solving 1.75 + y = -1.952562419 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 = -1.952562419 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = -1.952562419 + -1.75 y = -1.952562419 + -1.75 Combine like terms: -1.952562419 + -1.75 = -3.702562419 y = -3.702562419 Simplifying y = -3.702562419Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.202562419, -3.702562419}
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