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Simplifying 5y(y + -3) = 3y + -15 Reorder the terms: 5y(-3 + y) = 3y + -15 (-3 * 5y + y * 5y) = 3y + -15 (-15y + 5y2) = 3y + -15 Reorder the terms: -15y + 5y2 = -15 + 3y Solving -15y + 5y2 = -15 + 3y Solving for variable 'y'. Reorder the terms: 15 + -15y + -3y + 5y2 = -15 + 3y + 15 + -3y Combine like terms: -15y + -3y = -18y 15 + -18y + 5y2 = -15 + 3y + 15 + -3y Reorder the terms: 15 + -18y + 5y2 = -15 + 15 + 3y + -3y Combine like terms: -15 + 15 = 0 15 + -18y + 5y2 = 0 + 3y + -3y 15 + -18y + 5y2 = 3y + -3y Combine like terms: 3y + -3y = 0 15 + -18y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3 + -3.6y + y2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -3.6y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + -3.6y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -3.6y + y2 = 0 + -3 -3.6y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 -3.6y + y2 = -3 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 = -3 + 3.24 Reorder the terms: 3.24 + -3.6y + y2 = -3 + 3.24 Combine like terms: -3 + 3.24 = 0.24 3.24 + -3.6y + y2 = 0.24 Factor a perfect square on the left side: (y + -1.8)(y + -1.8) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (y + -1.8) equal to 0.489897949 and -0.489897949.Subproblem 1
y + -1.8 = 0.489897949 Simplifying y + -1.8 = 0.489897949 Reorder the terms: -1.8 + y = 0.489897949 Solving -1.8 + y = 0.489897949 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 = 0.489897949 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + y = 0.489897949 + 1.8 y = 0.489897949 + 1.8 Combine like terms: 0.489897949 + 1.8 = 2.289897949 y = 2.289897949 Simplifying y = 2.289897949Subproblem 2
y + -1.8 = -0.489897949 Simplifying y + -1.8 = -0.489897949 Reorder the terms: -1.8 + y = -0.489897949 Solving -1.8 + y = -0.489897949 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 = -0.489897949 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + y = -0.489897949 + 1.8 y = -0.489897949 + 1.8 Combine like terms: -0.489897949 + 1.8 = 1.310102051 y = 1.310102051 Simplifying y = 1.310102051Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.289897949, 1.310102051}
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