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Simplifying 7y2 + -9y + 8 + -15y2 + -9y + 5 = 0 Reorder the terms: 8 + 5 + -9y + -9y + 7y2 + -15y2 = 0 Combine like terms: 8 + 5 = 13 13 + -9y + -9y + 7y2 + -15y2 = 0 Combine like terms: -9y + -9y = -18y 13 + -18y + 7y2 + -15y2 = 0 Combine like terms: 7y2 + -15y2 = -8y2 13 + -18y + -8y2 = 0 Solving 13 + -18y + -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'. -1.625 + 2.25y + y2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 2.25y + 1.625 + y2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 2.25y + y2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 2.25y + y2 = 0 + 1.625 2.25y + y2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 2.25y + y2 = 1.625 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 = 1.625 + 1.265625 Reorder the terms: 1.265625 + 2.25y + y2 = 1.625 + 1.265625 Combine like terms: 1.625 + 1.265625 = 2.890625 1.265625 + 2.25y + y2 = 2.890625 Factor a perfect square on the left side: (y + 1.125)(y + 1.125) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (y + 1.125) equal to 1.700183814 and -1.700183814.Subproblem 1
y + 1.125 = 1.700183814 Simplifying y + 1.125 = 1.700183814 Reorder the terms: 1.125 + y = 1.700183814 Solving 1.125 + y = 1.700183814 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 = 1.700183814 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + y = 1.700183814 + -1.125 y = 1.700183814 + -1.125 Combine like terms: 1.700183814 + -1.125 = 0.575183814 y = 0.575183814 Simplifying y = 0.575183814Subproblem 2
y + 1.125 = -1.700183814 Simplifying y + 1.125 = -1.700183814 Reorder the terms: 1.125 + y = -1.700183814 Solving 1.125 + y = -1.700183814 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 = -1.700183814 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + y = -1.700183814 + -1.125 y = -1.700183814 + -1.125 Combine like terms: -1.700183814 + -1.125 = -2.825183814 y = -2.825183814 Simplifying y = -2.825183814Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.575183814, -2.825183814}
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