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Simplifying 0.4y(y + -6) = 0.2 Reorder the terms: 0.4y(-6 + y) = 0.2 (-6 * 0.4y + y * 0.4y) = 0.2 (-2.4y + 0.4y2) = 0.2 Solving -2.4y + 0.4y2 = 0.2 Solving for variable 'y'. Reorder the terms: -0.2 + -2.4y + 0.4y2 = 0.2 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 -0.2 + -2.4y + 0.4y2 = 0.0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. -0.5 + -6y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -6y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -6y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -6y + y2 = 0 + 0.5 -6y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -6y + y2 = 0.5 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = 0.5 + 9 Reorder the terms: 9 + -6y + y2 = 0.5 + 9 Combine like terms: 0.5 + 9 = 9.5 9 + -6y + y2 = 9.5 Factor a perfect square on the left side: (y + -3)(y + -3) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (y + -3) equal to 3.082207001 and -3.082207001.Subproblem 1
y + -3 = 3.082207001 Simplifying y + -3 = 3.082207001 Reorder the terms: -3 + y = 3.082207001 Solving -3 + y = 3.082207001 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 3.082207001 + 3 Combine like terms: -3 + 3 = 0 0 + y = 3.082207001 + 3 y = 3.082207001 + 3 Combine like terms: 3.082207001 + 3 = 6.082207001 y = 6.082207001 Simplifying y = 6.082207001Subproblem 2
y + -3 = -3.082207001 Simplifying y + -3 = -3.082207001 Reorder the terms: -3 + y = -3.082207001 Solving -3 + y = -3.082207001 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -3.082207001 + 3 Combine like terms: -3 + 3 = 0 0 + y = -3.082207001 + 3 y = -3.082207001 + 3 Combine like terms: -3.082207001 + 3 = -0.082207001 y = -0.082207001 Simplifying y = -0.082207001Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.082207001, -0.082207001}
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