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Simplifying -10y2 + 31y + 15 = 0 Reorder the terms: 15 + 31y + -10y2 = 0 Solving 15 + 31y + -10y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -1.5 + -3.1y + y2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -3.1y + 1.5 + y2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -3.1y + y2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -3.1y + y2 = 0 + 1.5 -3.1y + y2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -3.1y + y2 = 1.5 The y term is -3.1y. Take half its coefficient (-1.55). Square it (2.4025) and add it to both sides. Add '2.4025' to each side of the equation. -3.1y + 2.4025 + y2 = 1.5 + 2.4025 Reorder the terms: 2.4025 + -3.1y + y2 = 1.5 + 2.4025 Combine like terms: 1.5 + 2.4025 = 3.9025 2.4025 + -3.1y + y2 = 3.9025 Factor a perfect square on the left side: (y + -1.55)(y + -1.55) = 3.9025 Calculate the square root of the right side: 1.975474627 Break this problem into two subproblems by setting (y + -1.55) equal to 1.975474627 and -1.975474627.Subproblem 1
y + -1.55 = 1.975474627 Simplifying y + -1.55 = 1.975474627 Reorder the terms: -1.55 + y = 1.975474627 Solving -1.55 + y = 1.975474627 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + y = 1.975474627 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + y = 1.975474627 + 1.55 y = 1.975474627 + 1.55 Combine like terms: 1.975474627 + 1.55 = 3.525474627 y = 3.525474627 Simplifying y = 3.525474627Subproblem 2
y + -1.55 = -1.975474627 Simplifying y + -1.55 = -1.975474627 Reorder the terms: -1.55 + y = -1.975474627 Solving -1.55 + y = -1.975474627 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + y = -1.975474627 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + y = -1.975474627 + 1.55 y = -1.975474627 + 1.55 Combine like terms: -1.975474627 + 1.55 = -0.425474627 y = -0.425474627 Simplifying y = -0.425474627Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.525474627, -0.425474627}
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