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Simplifying (3y * 3y) + -1(5 + 5) + y = 25 Reorder the terms for easier multiplication: (3 * 3y * y) + -1(5 + 5) + y = 25 Multiply 3 * 3 (9y * y) + -1(5 + 5) + y = 25 Multiply y * y (9y2) + -1(5 + 5) + y = 25 Combine like terms: 5 + 5 = 10 (9y2) + -1(10) + y = 25 Multiply -1 * 10 (9y2) + -10 + y = 25 Reorder the terms: -10 + y + (9y2) = 25 Solving -10 + y + (9y2) = 25 Solving for variable 'y'. Reorder the terms: -10 + -25 + y + (9y2) = 25 + -25 Combine like terms: -10 + -25 = -35 -35 + y + (9y2) = 25 + -25 Combine like terms: 25 + -25 = 0 -35 + y + (9y2) = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.888888889 + 0.1111111111y + y2 = 0 Move the constant term to the right: Add '3.888888889' to each side of the equation. -3.888888889 + 0.1111111111y + 3.888888889 + y2 = 0 + 3.888888889 Reorder the terms: -3.888888889 + 3.888888889 + 0.1111111111y + y2 = 0 + 3.888888889 Combine like terms: -3.888888889 + 3.888888889 = 0.000000000 0.000000000 + 0.1111111111y + y2 = 0 + 3.888888889 0.1111111111y + y2 = 0 + 3.888888889 Combine like terms: 0 + 3.888888889 = 3.888888889 0.1111111111y + y2 = 3.888888889 The y term is y. 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. 0.1111111111y + 0.25 + y2 = 3.888888889 + 0.25 Reorder the terms: 0.25 + 0.1111111111y + y2 = 3.888888889 + 0.25 Combine like terms: 3.888888889 + 0.25 = 4.138888889 0.25 + 0.1111111111y + y2 = 4.138888889 Factor a perfect square on the left side: ((y) + 0.5)((y) + 0.5) = 4.138888889 Calculate the square root of the right side: 2.034425936 Break this problem into two subproblems by setting ((y) + 0.5) equal to 2.034425936 and -2.034425936.Subproblem 1
(y) + 0.5 = 2.034425936 Simplifying (y) + 0.5 = 2.034425936 y + 0.5 = 2.034425936 Reorder the terms: 0.5 + y = 2.034425936 Solving 0.5 + y = 2.034425936 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 = 2.034425936 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 2.034425936 + -0.5 y = 2.034425936 + -0.5 Combine like terms: 2.034425936 + -0.5 = 1.534425936 y = 1.534425936 Simplifying y = 1.534425936Subproblem 2
(y) + 0.5 = -2.034425936 Simplifying (y) + 0.5 = -2.034425936 y + 0.5 = -2.034425936 Reorder the terms: 0.5 + y = -2.034425936 Solving 0.5 + y = -2.034425936 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 = -2.034425936 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -2.034425936 + -0.5 y = -2.034425936 + -0.5 Combine like terms: -2.034425936 + -0.5 = -2.534425936 y = -2.534425936 Simplifying y = -2.534425936Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.534425936, -2.534425936}
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