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Simplifying 8y2 + 18y = 137 Reorder the terms: 18y + 8y2 = 137 Solving 18y + 8y2 = 137 Solving for variable 'y'. Reorder the terms: -137 + 18y + 8y2 = 137 + -137 Combine like terms: 137 + -137 = 0 -137 + 18y + 8y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -17.125 + 2.25y + y2 = 0 Move the constant term to the right: Add '17.125' to each side of the equation. -17.125 + 2.25y + 17.125 + y2 = 0 + 17.125 Reorder the terms: -17.125 + 17.125 + 2.25y + y2 = 0 + 17.125 Combine like terms: -17.125 + 17.125 = 0.000 0.000 + 2.25y + y2 = 0 + 17.125 2.25y + y2 = 0 + 17.125 Combine like terms: 0 + 17.125 = 17.125 2.25y + y2 = 17.125 The y term is 2.25y. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25y + 1.265625 + y2 = 17.125 + 1.265625 Reorder the terms: 1.265625 + 2.25y + y2 = 17.125 + 1.265625 Combine like terms: 17.125 + 1.265625 = 18.390625 1.265625 + 2.25y + y2 = 18.390625 Factor a perfect square on the left side: (y + 1.125)(y + 1.125) = 18.390625 Calculate the square root of the right side: 4.2884292 Break this problem into two subproblems by setting (y + 1.125) equal to 4.2884292 and -4.2884292.Subproblem 1
y + 1.125 = 4.2884292 Simplifying y + 1.125 = 4.2884292 Reorder the terms: 1.125 + y = 4.2884292 Solving 1.125 + y = 4.2884292 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + y = 4.2884292 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + y = 4.2884292 + -1.125 y = 4.2884292 + -1.125 Combine like terms: 4.2884292 + -1.125 = 3.1634292 y = 3.1634292 Simplifying y = 3.1634292Subproblem 2
y + 1.125 = -4.2884292 Simplifying y + 1.125 = -4.2884292 Reorder the terms: 1.125 + y = -4.2884292 Solving 1.125 + y = -4.2884292 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + y = -4.2884292 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + y = -4.2884292 + -1.125 y = -4.2884292 + -1.125 Combine like terms: -4.2884292 + -1.125 = -5.4134292 y = -5.4134292 Simplifying y = -5.4134292Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.1634292, -5.4134292}
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