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Simplifying 5y2 = 18y + -4 Reorder the terms: 5y2 = -4 + 18y Solving 5y2 = -4 + 18y Solving for variable 'y'. Reorder the terms: 4 + -18y + 5y2 = -4 + 18y + 4 + -18y Reorder the terms: 4 + -18y + 5y2 = -4 + 4 + 18y + -18y Combine like terms: -4 + 4 = 0 4 + -18y + 5y2 = 0 + 18y + -18y 4 + -18y + 5y2 = 18y + -18y Combine like terms: 18y + -18y = 0 4 + -18y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -3.6y + y2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -3.6y + -0.8 + y2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -3.6y + y2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -3.6y + y2 = 0 + -0.8 -3.6y + y2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -3.6y + y2 = -0.8 The y term is -3.6y. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6y + 3.24 + y2 = -0.8 + 3.24 Reorder the terms: 3.24 + -3.6y + y2 = -0.8 + 3.24 Combine like terms: -0.8 + 3.24 = 2.44 3.24 + -3.6y + y2 = 2.44 Factor a perfect square on the left side: (y + -1.8)(y + -1.8) = 2.44 Calculate the square root of the right side: 1.562049935 Break this problem into two subproblems by setting (y + -1.8) equal to 1.562049935 and -1.562049935.Subproblem 1
y + -1.8 = 1.562049935 Simplifying y + -1.8 = 1.562049935 Reorder the terms: -1.8 + y = 1.562049935 Solving -1.8 + y = 1.562049935 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + y = 1.562049935 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + y = 1.562049935 + 1.8 y = 1.562049935 + 1.8 Combine like terms: 1.562049935 + 1.8 = 3.362049935 y = 3.362049935 Simplifying y = 3.362049935Subproblem 2
y + -1.8 = -1.562049935 Simplifying y + -1.8 = -1.562049935 Reorder the terms: -1.8 + y = -1.562049935 Solving -1.8 + y = -1.562049935 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + y = -1.562049935 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + y = -1.562049935 + 1.8 y = -1.562049935 + 1.8 Combine like terms: -1.562049935 + 1.8 = 0.237950065 y = 0.237950065 Simplifying y = 0.237950065Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.362049935, 0.237950065}
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