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Simplifying 8y2 + -37y + 5 = 0 Reorder the terms: 5 + -37y + 8y2 = 0 Solving 5 + -37y + 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'. 0.625 + -4.625y + y2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -4.625y + -0.625 + y2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -4.625y + y2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -4.625y + y2 = 0 + -0.625 -4.625y + y2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -4.625y + y2 = -0.625 The y term is -4.625y. Take half its coefficient (-2.3125). Square it (5.34765625) and add it to both sides. Add '5.34765625' to each side of the equation. -4.625y + 5.34765625 + y2 = -0.625 + 5.34765625 Reorder the terms: 5.34765625 + -4.625y + y2 = -0.625 + 5.34765625 Combine like terms: -0.625 + 5.34765625 = 4.72265625 5.34765625 + -4.625y + y2 = 4.72265625 Factor a perfect square on the left side: (y + -2.3125)(y + -2.3125) = 4.72265625 Calculate the square root of the right side: 2.173167331 Break this problem into two subproblems by setting (y + -2.3125) equal to 2.173167331 and -2.173167331.Subproblem 1
y + -2.3125 = 2.173167331 Simplifying y + -2.3125 = 2.173167331 Reorder the terms: -2.3125 + y = 2.173167331 Solving -2.3125 + y = 2.173167331 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.3125' to each side of the equation. -2.3125 + 2.3125 + y = 2.173167331 + 2.3125 Combine like terms: -2.3125 + 2.3125 = 0.0000 0.0000 + y = 2.173167331 + 2.3125 y = 2.173167331 + 2.3125 Combine like terms: 2.173167331 + 2.3125 = 4.485667331 y = 4.485667331 Simplifying y = 4.485667331Subproblem 2
y + -2.3125 = -2.173167331 Simplifying y + -2.3125 = -2.173167331 Reorder the terms: -2.3125 + y = -2.173167331 Solving -2.3125 + y = -2.173167331 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.3125' to each side of the equation. -2.3125 + 2.3125 + y = -2.173167331 + 2.3125 Combine like terms: -2.3125 + 2.3125 = 0.0000 0.0000 + y = -2.173167331 + 2.3125 y = -2.173167331 + 2.3125 Combine like terms: -2.173167331 + 2.3125 = 0.139332669 y = 0.139332669 Simplifying y = 0.139332669Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.485667331, 0.139332669}
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