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Simplifying y2 + -3.3y + -10 = 0 Reorder the terms: -10 + -3.3y + y2 = 0 Solving -10 + -3.3y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -3.3y + 10 + y2 = 0 + 10 Reorder the terms: -10 + 10 + -3.3y + y2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3.3y + y2 = 0 + 10 -3.3y + y2 = 0 + 10 Combine like terms: 0 + 10 = 10 -3.3y + y2 = 10 The y term is -3.3y. Take half its coefficient (-1.65). Square it (2.7225) and add it to both sides. Add '2.7225' to each side of the equation. -3.3y + 2.7225 + y2 = 10 + 2.7225 Reorder the terms: 2.7225 + -3.3y + y2 = 10 + 2.7225 Combine like terms: 10 + 2.7225 = 12.7225 2.7225 + -3.3y + y2 = 12.7225 Factor a perfect square on the left side: (y + -1.65)(y + -1.65) = 12.7225 Calculate the square root of the right side: 3.566861365 Break this problem into two subproblems by setting (y + -1.65) equal to 3.566861365 and -3.566861365.Subproblem 1
y + -1.65 = 3.566861365 Simplifying y + -1.65 = 3.566861365 Reorder the terms: -1.65 + y = 3.566861365 Solving -1.65 + y = 3.566861365 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.65' to each side of the equation. -1.65 + 1.65 + y = 3.566861365 + 1.65 Combine like terms: -1.65 + 1.65 = 0.00 0.00 + y = 3.566861365 + 1.65 y = 3.566861365 + 1.65 Combine like terms: 3.566861365 + 1.65 = 5.216861365 y = 5.216861365 Simplifying y = 5.216861365Subproblem 2
y + -1.65 = -3.566861365 Simplifying y + -1.65 = -3.566861365 Reorder the terms: -1.65 + y = -3.566861365 Solving -1.65 + y = -3.566861365 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.65' to each side of the equation. -1.65 + 1.65 + y = -3.566861365 + 1.65 Combine like terms: -1.65 + 1.65 = 0.00 0.00 + y = -3.566861365 + 1.65 y = -3.566861365 + 1.65 Combine like terms: -3.566861365 + 1.65 = -1.916861365 y = -1.916861365 Simplifying y = -1.916861365Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.216861365, -1.916861365}
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