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Simplifying 12y + 5y(y + -6) = 4 Reorder the terms: 12y + 5y(-6 + y) = 4 12y + (-6 * 5y + y * 5y) = 4 12y + (-30y + 5y2) = 4 Combine like terms: 12y + -30y = -18y -18y + 5y2 = 4 Solving -18y + 5y2 = 4 Solving for variable 'y'. Reorder the terms: -4 + -18y + 5y2 = 4 + -4 Combine like terms: 4 + -4 = 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 = 4.04 3.24 + -3.6y + y2 = 4.04 Factor a perfect square on the left side: (y + -1.8)(y + -1.8) = 4.04 Calculate the square root of the right side: 2.009975124 Break this problem into two subproblems by setting (y + -1.8) equal to 2.009975124 and -2.009975124.Subproblem 1
y + -1.8 = 2.009975124 Simplifying y + -1.8 = 2.009975124 Reorder the terms: -1.8 + y = 2.009975124 Solving -1.8 + y = 2.009975124 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 = 2.009975124 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + y = 2.009975124 + 1.8 y = 2.009975124 + 1.8 Combine like terms: 2.009975124 + 1.8 = 3.809975124 y = 3.809975124 Simplifying y = 3.809975124Subproblem 2
y + -1.8 = -2.009975124 Simplifying y + -1.8 = -2.009975124 Reorder the terms: -1.8 + y = -2.009975124 Solving -1.8 + y = -2.009975124 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 = -2.009975124 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + y = -2.009975124 + 1.8 y = -2.009975124 + 1.8 Combine like terms: -2.009975124 + 1.8 = -0.209975124 y = -0.209975124 Simplifying y = -0.209975124Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.809975124, -0.209975124}
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