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Simplifying y(5y + -9) = 4 Reorder the terms: y(-9 + 5y) = 4 (-9 * y + 5y * y) = 4 (-9y + 5y2) = 4 Solving -9y + 5y2 = 4 Solving for variable 'y'. Reorder the terms: -4 + -9y + 5y2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -9y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -1.8y + y2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -1.8y + 0.8 + y2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -1.8y + y2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -1.8y + y2 = 0 + 0.8 -1.8y + y2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -1.8y + y2 = 0.8 The y term is -1.8y. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8y + 0.81 + y2 = 0.8 + 0.81 Reorder the terms: 0.81 + -1.8y + y2 = 0.8 + 0.81 Combine like terms: 0.8 + 0.81 = 1.61 0.81 + -1.8y + y2 = 1.61 Factor a perfect square on the left side: (y + -0.9)(y + -0.9) = 1.61 Calculate the square root of the right side: 1.268857754 Break this problem into two subproblems by setting (y + -0.9) equal to 1.268857754 and -1.268857754.Subproblem 1
y + -0.9 = 1.268857754 Simplifying y + -0.9 = 1.268857754 Reorder the terms: -0.9 + y = 1.268857754 Solving -0.9 + y = 1.268857754 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + y = 1.268857754 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + y = 1.268857754 + 0.9 y = 1.268857754 + 0.9 Combine like terms: 1.268857754 + 0.9 = 2.168857754 y = 2.168857754 Simplifying y = 2.168857754Subproblem 2
y + -0.9 = -1.268857754 Simplifying y + -0.9 = -1.268857754 Reorder the terms: -0.9 + y = -1.268857754 Solving -0.9 + y = -1.268857754 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + y = -1.268857754 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + y = -1.268857754 + 0.9 y = -1.268857754 + 0.9 Combine like terms: -1.268857754 + 0.9 = -0.368857754 y = -0.368857754 Simplifying y = -0.368857754Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.168857754, -0.368857754}
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