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Simplifying -0.69y2 = 2.7y + 1.8 Reorder the terms: -0.69y2 = 1.8 + 2.7y Solving -0.69y2 = 1.8 + 2.7y Solving for variable 'y'. Reorder the terms: -1.8 + -2.7y + -0.69y2 = 1.8 + 2.7y + -1.8 + -2.7y Reorder the terms: -1.8 + -2.7y + -0.69y2 = 1.8 + -1.8 + 2.7y + -2.7y Combine like terms: 1.8 + -1.8 = 0.0 -1.8 + -2.7y + -0.69y2 = 0.0 + 2.7y + -2.7y -1.8 + -2.7y + -0.69y2 = 2.7y + -2.7y Combine like terms: 2.7y + -2.7y = 0.0 -1.8 + -2.7y + -0.69y2 = 0.0 Begin completing the square. Divide all terms by -0.69 the coefficient of the squared term: Divide each side by '-0.69'. 2.608695652 + 3.913043478y + y2 = 0 Move the constant term to the right: Add '-2.608695652' to each side of the equation. 2.608695652 + 3.913043478y + -2.608695652 + y2 = 0 + -2.608695652 Reorder the terms: 2.608695652 + -2.608695652 + 3.913043478y + y2 = 0 + -2.608695652 Combine like terms: 2.608695652 + -2.608695652 = 0.000000000 0.000000000 + 3.913043478y + y2 = 0 + -2.608695652 3.913043478y + y2 = 0 + -2.608695652 Combine like terms: 0 + -2.608695652 = -2.608695652 3.913043478y + y2 = -2.608695652 The y term is 3.913043478y. Take half its coefficient (1.956521739). Square it (3.827977315) and add it to both sides. Add '3.827977315' to each side of the equation. 3.913043478y + 3.827977315 + y2 = -2.608695652 + 3.827977315 Reorder the terms: 3.827977315 + 3.913043478y + y2 = -2.608695652 + 3.827977315 Combine like terms: -2.608695652 + 3.827977315 = 1.219281663 3.827977315 + 3.913043478y + y2 = 1.219281663 Factor a perfect square on the left side: (y + 1.956521739)(y + 1.956521739) = 1.219281663 Calculate the square root of the right side: 1.104210878 Break this problem into two subproblems by setting (y + 1.956521739) equal to 1.104210878 and -1.104210878.Subproblem 1
y + 1.956521739 = 1.104210878 Simplifying y + 1.956521739 = 1.104210878 Reorder the terms: 1.956521739 + y = 1.104210878 Solving 1.956521739 + y = 1.104210878 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.956521739' to each side of the equation. 1.956521739 + -1.956521739 + y = 1.104210878 + -1.956521739 Combine like terms: 1.956521739 + -1.956521739 = 0.000000000 0.000000000 + y = 1.104210878 + -1.956521739 y = 1.104210878 + -1.956521739 Combine like terms: 1.104210878 + -1.956521739 = -0.852310861 y = -0.852310861 Simplifying y = -0.852310861Subproblem 2
y + 1.956521739 = -1.104210878 Simplifying y + 1.956521739 = -1.104210878 Reorder the terms: 1.956521739 + y = -1.104210878 Solving 1.956521739 + y = -1.104210878 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.956521739' to each side of the equation. 1.956521739 + -1.956521739 + y = -1.104210878 + -1.956521739 Combine like terms: 1.956521739 + -1.956521739 = 0.000000000 0.000000000 + y = -1.104210878 + -1.956521739 y = -1.104210878 + -1.956521739 Combine like terms: -1.104210878 + -1.956521739 = -3.060732617 y = -3.060732617 Simplifying y = -3.060732617Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.852310861, -3.060732617}
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