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Simplifying 5y2 + -9y = 3 Reorder the terms: -9y + 5y2 = 3 Solving -9y + 5y2 = 3 Solving for variable 'y'. Reorder the terms: -3 + -9y + 5y2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -9y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -1.8y + y2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.8y + 0.6 + y2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.8y + y2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.8y + y2 = 0 + 0.6 -1.8y + y2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.8y + y2 = 0.6 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 = 0.6 + 0.81 Reorder the terms: 0.81 + -1.8y + y2 = 0.6 + 0.81 Combine like terms: 0.6 + 0.81 = 1.41 0.81 + -1.8y + y2 = 1.41 Factor a perfect square on the left side: (y + -0.9)(y + -0.9) = 1.41 Calculate the square root of the right side: 1.187434209 Break this problem into two subproblems by setting (y + -0.9) equal to 1.187434209 and -1.187434209.Subproblem 1
y + -0.9 = 1.187434209 Simplifying y + -0.9 = 1.187434209 Reorder the terms: -0.9 + y = 1.187434209 Solving -0.9 + y = 1.187434209 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 = 1.187434209 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + y = 1.187434209 + 0.9 y = 1.187434209 + 0.9 Combine like terms: 1.187434209 + 0.9 = 2.087434209 y = 2.087434209 Simplifying y = 2.087434209Subproblem 2
y + -0.9 = -1.187434209 Simplifying y + -0.9 = -1.187434209 Reorder the terms: -0.9 + y = -1.187434209 Solving -0.9 + y = -1.187434209 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 = -1.187434209 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + y = -1.187434209 + 0.9 y = -1.187434209 + 0.9 Combine like terms: -1.187434209 + 0.9 = -0.287434209 y = -0.287434209 Simplifying y = -0.287434209Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.087434209, -0.287434209}
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