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Simplifying (8y + -5) * 6y + -7 = 0 Reorder the terms: (-5 + 8y) * 6y + -7 = 0 Reorder the terms for easier multiplication: 6y(-5 + 8y) + -7 = 0 (-5 * 6y + 8y * 6y) + -7 = 0 (-30y + 48y2) + -7 = 0 Reorder the terms: -7 + -30y + 48y2 = 0 Solving -7 + -30y + 48y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.1458333333 + -0.625y + y2 = 0 Move the constant term to the right: Add '0.1458333333' to each side of the equation. -0.1458333333 + -0.625y + 0.1458333333 + y2 = 0 + 0.1458333333 Reorder the terms: -0.1458333333 + 0.1458333333 + -0.625y + y2 = 0 + 0.1458333333 Combine like terms: -0.1458333333 + 0.1458333333 = 0.0000000000 0.0000000000 + -0.625y + y2 = 0 + 0.1458333333 -0.625y + y2 = 0 + 0.1458333333 Combine like terms: 0 + 0.1458333333 = 0.1458333333 -0.625y + y2 = 0.1458333333 The y term is -0.625y. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625y + 0.09765625 + y2 = 0.1458333333 + 0.09765625 Reorder the terms: 0.09765625 + -0.625y + y2 = 0.1458333333 + 0.09765625 Combine like terms: 0.1458333333 + 0.09765625 = 0.2434895833 0.09765625 + -0.625y + y2 = 0.2434895833 Factor a perfect square on the left side: (y + -0.3125)(y + -0.3125) = 0.2434895833 Calculate the square root of the right side: 0.493446637 Break this problem into two subproblems by setting (y + -0.3125) equal to 0.493446637 and -0.493446637.Subproblem 1
y + -0.3125 = 0.493446637 Simplifying y + -0.3125 = 0.493446637 Reorder the terms: -0.3125 + y = 0.493446637 Solving -0.3125 + y = 0.493446637 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + y = 0.493446637 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + y = 0.493446637 + 0.3125 y = 0.493446637 + 0.3125 Combine like terms: 0.493446637 + 0.3125 = 0.805946637 y = 0.805946637 Simplifying y = 0.805946637Subproblem 2
y + -0.3125 = -0.493446637 Simplifying y + -0.3125 = -0.493446637 Reorder the terms: -0.3125 + y = -0.493446637 Solving -0.3125 + y = -0.493446637 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + y = -0.493446637 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + y = -0.493446637 + 0.3125 y = -0.493446637 + 0.3125 Combine like terms: -0.493446637 + 0.3125 = -0.180946637 y = -0.180946637 Simplifying y = -0.180946637Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.805946637, -0.180946637}
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