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Simplifying 5y2 + -24y + 9 = 0 Reorder the terms: 9 + -24y + 5y2 = 0 Solving 9 + -24y + 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'. 1.8 + -4.8y + y2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -4.8y + -1.8 + y2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -4.8y + y2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -4.8y + y2 = 0 + -1.8 -4.8y + y2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -4.8y + y2 = -1.8 The y term is -4.8y. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8y + 5.76 + y2 = -1.8 + 5.76 Reorder the terms: 5.76 + -4.8y + y2 = -1.8 + 5.76 Combine like terms: -1.8 + 5.76 = 3.96 5.76 + -4.8y + y2 = 3.96 Factor a perfect square on the left side: (y + -2.4)(y + -2.4) = 3.96 Calculate the square root of the right side: 1.989974874 Break this problem into two subproblems by setting (y + -2.4) equal to 1.989974874 and -1.989974874.Subproblem 1
y + -2.4 = 1.989974874 Simplifying y + -2.4 = 1.989974874 Reorder the terms: -2.4 + y = 1.989974874 Solving -2.4 + y = 1.989974874 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + y = 1.989974874 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + y = 1.989974874 + 2.4 y = 1.989974874 + 2.4 Combine like terms: 1.989974874 + 2.4 = 4.389974874 y = 4.389974874 Simplifying y = 4.389974874Subproblem 2
y + -2.4 = -1.989974874 Simplifying y + -2.4 = -1.989974874 Reorder the terms: -2.4 + y = -1.989974874 Solving -2.4 + y = -1.989974874 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + y = -1.989974874 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + y = -1.989974874 + 2.4 y = -1.989974874 + 2.4 Combine like terms: -1.989974874 + 2.4 = 0.410025126 y = 0.410025126 Simplifying y = 0.410025126Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.389974874, 0.410025126}
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