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Simplifying 10y2 + -33y + -14 = 0 Reorder the terms: -14 + -33y + 10y2 = 0 Solving -14 + -33y + 10y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.4 + -3.3y + y2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -3.3y + 1.4 + y2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -3.3y + y2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -3.3y + y2 = 0 + 1.4 -3.3y + y2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -3.3y + y2 = 1.4 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 = 1.4 + 2.7225 Reorder the terms: 2.7225 + -3.3y + y2 = 1.4 + 2.7225 Combine like terms: 1.4 + 2.7225 = 4.1225 2.7225 + -3.3y + y2 = 4.1225 Factor a perfect square on the left side: (y + -1.65)(y + -1.65) = 4.1225 Calculate the square root of the right side: 2.03039405 Break this problem into two subproblems by setting (y + -1.65) equal to 2.03039405 and -2.03039405.Subproblem 1
y + -1.65 = 2.03039405 Simplifying y + -1.65 = 2.03039405 Reorder the terms: -1.65 + y = 2.03039405 Solving -1.65 + y = 2.03039405 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 = 2.03039405 + 1.65 Combine like terms: -1.65 + 1.65 = 0.00 0.00 + y = 2.03039405 + 1.65 y = 2.03039405 + 1.65 Combine like terms: 2.03039405 + 1.65 = 3.68039405 y = 3.68039405 Simplifying y = 3.68039405Subproblem 2
y + -1.65 = -2.03039405 Simplifying y + -1.65 = -2.03039405 Reorder the terms: -1.65 + y = -2.03039405 Solving -1.65 + y = -2.03039405 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 = -2.03039405 + 1.65 Combine like terms: -1.65 + 1.65 = 0.00 0.00 + y = -2.03039405 + 1.65 y = -2.03039405 + 1.65 Combine like terms: -2.03039405 + 1.65 = -0.38039405 y = -0.38039405 Simplifying y = -0.38039405Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.68039405, -0.38039405}
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