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Simplifying 8y2 + -21y + 9 = 0 Reorder the terms: 9 + -21y + 8y2 = 0 Solving 9 + -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'. 1.125 + -2.625y + y2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -2.625y + -1.125 + y2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -2.625y + y2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -2.625y + y2 = 0 + -1.125 -2.625y + y2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -2.625y + y2 = -1.125 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 = -1.125 + 1.72265625 Reorder the terms: 1.72265625 + -2.625y + y2 = -1.125 + 1.72265625 Combine like terms: -1.125 + 1.72265625 = 0.59765625 1.72265625 + -2.625y + y2 = 0.59765625 Factor a perfect square on the left side: (y + -1.3125)(y + -1.3125) = 0.59765625 Calculate the square root of the right side: 0.773082305 Break this problem into two subproblems by setting (y + -1.3125) equal to 0.773082305 and -0.773082305.Subproblem 1
y + -1.3125 = 0.773082305 Simplifying y + -1.3125 = 0.773082305 Reorder the terms: -1.3125 + y = 0.773082305 Solving -1.3125 + y = 0.773082305 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 = 0.773082305 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + y = 0.773082305 + 1.3125 y = 0.773082305 + 1.3125 Combine like terms: 0.773082305 + 1.3125 = 2.085582305 y = 2.085582305 Simplifying y = 2.085582305Subproblem 2
y + -1.3125 = -0.773082305 Simplifying y + -1.3125 = -0.773082305 Reorder the terms: -1.3125 + y = -0.773082305 Solving -1.3125 + y = -0.773082305 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 = -0.773082305 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + y = -0.773082305 + 1.3125 y = -0.773082305 + 1.3125 Combine like terms: -0.773082305 + 1.3125 = 0.539417695 y = 0.539417695 Simplifying y = 0.539417695Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.085582305, 0.539417695}
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