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Simplifying 5y2 + -24y + 15 = 0 Reorder the terms: 15 + -24y + 5y2 = 0 Solving 15 + -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'. 3 + -4.8y + y2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -4.8y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + -4.8y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4.8y + y2 = 0 + -3 -4.8y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4.8y + y2 = -3 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 = -3 + 5.76 Reorder the terms: 5.76 + -4.8y + y2 = -3 + 5.76 Combine like terms: -3 + 5.76 = 2.76 5.76 + -4.8y + y2 = 2.76 Factor a perfect square on the left side: (y + -2.4)(y + -2.4) = 2.76 Calculate the square root of the right side: 1.661324773 Break this problem into two subproblems by setting (y + -2.4) equal to 1.661324773 and -1.661324773.Subproblem 1
y + -2.4 = 1.661324773 Simplifying y + -2.4 = 1.661324773 Reorder the terms: -2.4 + y = 1.661324773 Solving -2.4 + y = 1.661324773 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 = 1.661324773 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + y = 1.661324773 + 2.4 y = 1.661324773 + 2.4 Combine like terms: 1.661324773 + 2.4 = 4.061324773 y = 4.061324773 Simplifying y = 4.061324773Subproblem 2
y + -2.4 = -1.661324773 Simplifying y + -2.4 = -1.661324773 Reorder the terms: -2.4 + y = -1.661324773 Solving -2.4 + y = -1.661324773 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 = -1.661324773 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + y = -1.661324773 + 2.4 y = -1.661324773 + 2.4 Combine like terms: -1.661324773 + 2.4 = 0.738675227 y = 0.738675227 Simplifying y = 0.738675227Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.061324773, 0.738675227}
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