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Simplifying -3(9 + 8y) * 2y = -5 Reorder the terms for easier multiplication: -3 * 2y(9 + 8y) = -5 Multiply -3 * 2 -6y(9 + 8y) = -5 (9 * -6y + 8y * -6y) = -5 (-54y + -48y2) = -5 Solving -54y + -48y2 = -5 Solving for variable 'y'. Reorder the terms: 5 + -54y + -48y2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + -54y + -48y2 = 0 Begin completing the square. Divide all terms by -48 the coefficient of the squared term: Divide each side by '-48'. -0.1041666667 + 1.125y + y2 = 0 Move the constant term to the right: Add '0.1041666667' to each side of the equation. -0.1041666667 + 1.125y + 0.1041666667 + y2 = 0 + 0.1041666667 Reorder the terms: -0.1041666667 + 0.1041666667 + 1.125y + y2 = 0 + 0.1041666667 Combine like terms: -0.1041666667 + 0.1041666667 = 0.0000000000 0.0000000000 + 1.125y + y2 = 0 + 0.1041666667 1.125y + y2 = 0 + 0.1041666667 Combine like terms: 0 + 0.1041666667 = 0.1041666667 1.125y + y2 = 0.1041666667 The y term is 1.125y. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125y + 0.31640625 + y2 = 0.1041666667 + 0.31640625 Reorder the terms: 0.31640625 + 1.125y + y2 = 0.1041666667 + 0.31640625 Combine like terms: 0.1041666667 + 0.31640625 = 0.4205729167 0.31640625 + 1.125y + y2 = 0.4205729167 Factor a perfect square on the left side: (y + 0.5625)(y + 0.5625) = 0.4205729167 Calculate the square root of the right side: 0.648515934 Break this problem into two subproblems by setting (y + 0.5625) equal to 0.648515934 and -0.648515934.Subproblem 1
y + 0.5625 = 0.648515934 Simplifying y + 0.5625 = 0.648515934 Reorder the terms: 0.5625 + y = 0.648515934 Solving 0.5625 + y = 0.648515934 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + y = 0.648515934 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + y = 0.648515934 + -0.5625 y = 0.648515934 + -0.5625 Combine like terms: 0.648515934 + -0.5625 = 0.086015934 y = 0.086015934 Simplifying y = 0.086015934Subproblem 2
y + 0.5625 = -0.648515934 Simplifying y + 0.5625 = -0.648515934 Reorder the terms: 0.5625 + y = -0.648515934 Solving 0.5625 + y = -0.648515934 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + y = -0.648515934 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + y = -0.648515934 + -0.5625 y = -0.648515934 + -0.5625 Combine like terms: -0.648515934 + -0.5625 = -1.211015934 y = -1.211015934 Simplifying y = -1.211015934Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.086015934, -1.211015934}
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