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Simplifying (8y2 + 21y + 8) = 0 Reorder the terms: (8 + 21y + 8y2) = 0 Remove parenthesis around (8 + 21y + 8y2) 8 + 21y + 8y2 = 0 Solving 8 + 21y + 8y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1 + 2.625y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.625y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + 2.625y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.625y + y2 = 0 + -1 2.625y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.625y + y2 = -1 The y term is 2.625y. Take half its coefficient (1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. 2.625y + 1.72265625 + y2 = -1 + 1.72265625 Reorder the terms: 1.72265625 + 2.625y + y2 = -1 + 1.72265625 Combine like terms: -1 + 1.72265625 = 0.72265625 1.72265625 + 2.625y + y2 = 0.72265625 Factor a perfect square on the left side: (y + 1.3125)(y + 1.3125) = 0.72265625 Calculate the square root of the right side: 0.850091907 Break this problem into two subproblems by setting (y + 1.3125) equal to 0.850091907 and -0.850091907.Subproblem 1
y + 1.3125 = 0.850091907 Simplifying y + 1.3125 = 0.850091907 Reorder the terms: 1.3125 + y = 0.850091907 Solving 1.3125 + y = 0.850091907 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.3125' to each side of the equation. 1.3125 + -1.3125 + y = 0.850091907 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + y = 0.850091907 + -1.3125 y = 0.850091907 + -1.3125 Combine like terms: 0.850091907 + -1.3125 = -0.462408093 y = -0.462408093 Simplifying y = -0.462408093Subproblem 2
y + 1.3125 = -0.850091907 Simplifying y + 1.3125 = -0.850091907 Reorder the terms: 1.3125 + y = -0.850091907 Solving 1.3125 + y = -0.850091907 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.3125' to each side of the equation. 1.3125 + -1.3125 + y = -0.850091907 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + y = -0.850091907 + -1.3125 y = -0.850091907 + -1.3125 Combine like terms: -0.850091907 + -1.3125 = -2.162591907 y = -2.162591907 Simplifying y = -2.162591907Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.462408093, -2.162591907}
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