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Simplifying 5y2 + -39y + -40 = 0 Reorder the terms: -40 + -39y + 5y2 = 0 Solving -40 + -39y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8 + -7.8y + y2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -7.8y + 8 + y2 = 0 + 8 Reorder the terms: -8 + 8 + -7.8y + y2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -7.8y + y2 = 0 + 8 -7.8y + y2 = 0 + 8 Combine like terms: 0 + 8 = 8 -7.8y + y2 = 8 The y term is -7.8y. Take half its coefficient (-3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. -7.8y + 15.21 + y2 = 8 + 15.21 Reorder the terms: 15.21 + -7.8y + y2 = 8 + 15.21 Combine like terms: 8 + 15.21 = 23.21 15.21 + -7.8y + y2 = 23.21 Factor a perfect square on the left side: (y + -3.9)(y + -3.9) = 23.21 Calculate the square root of the right side: 4.817675788 Break this problem into two subproblems by setting (y + -3.9) equal to 4.817675788 and -4.817675788.Subproblem 1
y + -3.9 = 4.817675788 Simplifying y + -3.9 = 4.817675788 Reorder the terms: -3.9 + y = 4.817675788 Solving -3.9 + y = 4.817675788 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + y = 4.817675788 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + y = 4.817675788 + 3.9 y = 4.817675788 + 3.9 Combine like terms: 4.817675788 + 3.9 = 8.717675788 y = 8.717675788 Simplifying y = 8.717675788Subproblem 2
y + -3.9 = -4.817675788 Simplifying y + -3.9 = -4.817675788 Reorder the terms: -3.9 + y = -4.817675788 Solving -3.9 + y = -4.817675788 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + y = -4.817675788 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + y = -4.817675788 + 3.9 y = -4.817675788 + 3.9 Combine like terms: -4.817675788 + 3.9 = -0.917675788 y = -0.917675788 Simplifying y = -0.917675788Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.717675788, -0.917675788}
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