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Simplifying y(5y + -6) = 38 Reorder the terms: y(-6 + 5y) = 38 (-6 * y + 5y * y) = 38 (-6y + 5y2) = 38 Solving -6y + 5y2 = 38 Solving for variable 'y'. Reorder the terms: -38 + -6y + 5y2 = 38 + -38 Combine like terms: 38 + -38 = 0 -38 + -6y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.6 + -1.2y + y2 = 0 Move the constant term to the right: Add '7.6' to each side of the equation. -7.6 + -1.2y + 7.6 + y2 = 0 + 7.6 Reorder the terms: -7.6 + 7.6 + -1.2y + y2 = 0 + 7.6 Combine like terms: -7.6 + 7.6 = 0.0 0.0 + -1.2y + y2 = 0 + 7.6 -1.2y + y2 = 0 + 7.6 Combine like terms: 0 + 7.6 = 7.6 -1.2y + y2 = 7.6 The y term is -1.2y. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2y + 0.36 + y2 = 7.6 + 0.36 Reorder the terms: 0.36 + -1.2y + y2 = 7.6 + 0.36 Combine like terms: 7.6 + 0.36 = 7.96 0.36 + -1.2y + y2 = 7.96 Factor a perfect square on the left side: (y + -0.6)(y + -0.6) = 7.96 Calculate the square root of the right side: 2.821347196 Break this problem into two subproblems by setting (y + -0.6) equal to 2.821347196 and -2.821347196.Subproblem 1
y + -0.6 = 2.821347196 Simplifying y + -0.6 = 2.821347196 Reorder the terms: -0.6 + y = 2.821347196 Solving -0.6 + y = 2.821347196 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + y = 2.821347196 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + y = 2.821347196 + 0.6 y = 2.821347196 + 0.6 Combine like terms: 2.821347196 + 0.6 = 3.421347196 y = 3.421347196 Simplifying y = 3.421347196Subproblem 2
y + -0.6 = -2.821347196 Simplifying y + -0.6 = -2.821347196 Reorder the terms: -0.6 + y = -2.821347196 Solving -0.6 + y = -2.821347196 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + y = -2.821347196 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + y = -2.821347196 + 0.6 y = -2.821347196 + 0.6 Combine like terms: -2.821347196 + 0.6 = -2.221347196 y = -2.221347196 Simplifying y = -2.221347196Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.421347196, -2.221347196}
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