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Simplifying 5(-3y + -1) + -6(6 + -5y) * y = -6 Reorder the terms: 5(-1 + -3y) + -6(6 + -5y) * y = -6 (-1 * 5 + -3y * 5) + -6(6 + -5y) * y = -6 (-5 + -15y) + -6(6 + -5y) * y = -6 Reorder the terms for easier multiplication: -5 + -15y + -6y(6 + -5y) = -6 -5 + -15y + (6 * -6y + -5y * -6y) = -6 -5 + -15y + (-36y + 30y2) = -6 Combine like terms: -15y + -36y = -51y -5 + -51y + 30y2 = -6 Solving -5 + -51y + 30y2 = -6 Solving for variable 'y'. Reorder the terms: -5 + 6 + -51y + 30y2 = -6 + 6 Combine like terms: -5 + 6 = 1 1 + -51y + 30y2 = -6 + 6 Combine like terms: -6 + 6 = 0 1 + -51y + 30y2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 0.03333333333 + -1.7y + y2 = 0.0 Move the constant term to the right: Add '-0.03333333333' to each side of the equation. 0.03333333333 + -1.7y + -0.03333333333 + y2 = 0.0 + -0.03333333333 Reorder the terms: 0.03333333333 + -0.03333333333 + -1.7y + y2 = 0.0 + -0.03333333333 Combine like terms: 0.03333333333 + -0.03333333333 = 0.00000000000 0.00000000000 + -1.7y + y2 = 0.0 + -0.03333333333 -1.7y + y2 = 0.0 + -0.03333333333 Combine like terms: 0.0 + -0.03333333333 = -0.03333333333 -1.7y + y2 = -0.03333333333 The y term is -1.7y. Take half its coefficient (-0.85). Square it (0.7225) and add it to both sides. Add '0.7225' to each side of the equation. -1.7y + 0.7225 + y2 = -0.03333333333 + 0.7225 Reorder the terms: 0.7225 + -1.7y + y2 = -0.03333333333 + 0.7225 Combine like terms: -0.03333333333 + 0.7225 = 0.68916666667 0.7225 + -1.7y + y2 = 0.68916666667 Factor a perfect square on the left side: (y + -0.85)(y + -0.85) = 0.68916666667 Calculate the square root of the right side: 0.830160627 Break this problem into two subproblems by setting (y + -0.85) equal to 0.830160627 and -0.830160627.Subproblem 1
y + -0.85 = 0.830160627 Simplifying y + -0.85 = 0.830160627 Reorder the terms: -0.85 + y = 0.830160627 Solving -0.85 + y = 0.830160627 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + y = 0.830160627 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + y = 0.830160627 + 0.85 y = 0.830160627 + 0.85 Combine like terms: 0.830160627 + 0.85 = 1.680160627 y = 1.680160627 Simplifying y = 1.680160627Subproblem 2
y + -0.85 = -0.830160627 Simplifying y + -0.85 = -0.830160627 Reorder the terms: -0.85 + y = -0.830160627 Solving -0.85 + y = -0.830160627 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + y = -0.830160627 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + y = -0.830160627 + 0.85 y = -0.830160627 + 0.85 Combine like terms: -0.830160627 + 0.85 = 0.019839373 y = 0.019839373 Simplifying y = 0.019839373Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.680160627, 0.019839373}
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