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Simplifying 25y2 + -33y + -14 = 0 Reorder the terms: -14 + -33y + 25y2 = 0 Solving -14 + -33y + 25y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.56 + -1.32y + y2 = 0 Move the constant term to the right: Add '0.56' to each side of the equation. -0.56 + -1.32y + 0.56 + y2 = 0 + 0.56 Reorder the terms: -0.56 + 0.56 + -1.32y + y2 = 0 + 0.56 Combine like terms: -0.56 + 0.56 = 0.00 0.00 + -1.32y + y2 = 0 + 0.56 -1.32y + y2 = 0 + 0.56 Combine like terms: 0 + 0.56 = 0.56 -1.32y + y2 = 0.56 The y term is -1.32y. Take half its coefficient (-0.66). Square it (0.4356) and add it to both sides. Add '0.4356' to each side of the equation. -1.32y + 0.4356 + y2 = 0.56 + 0.4356 Reorder the terms: 0.4356 + -1.32y + y2 = 0.56 + 0.4356 Combine like terms: 0.56 + 0.4356 = 0.9956 0.4356 + -1.32y + y2 = 0.9956 Factor a perfect square on the left side: (y + -0.66)(y + -0.66) = 0.9956 Calculate the square root of the right side: 0.997797575 Break this problem into two subproblems by setting (y + -0.66) equal to 0.997797575 and -0.997797575.Subproblem 1
y + -0.66 = 0.997797575 Simplifying y + -0.66 = 0.997797575 Reorder the terms: -0.66 + y = 0.997797575 Solving -0.66 + y = 0.997797575 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.66' to each side of the equation. -0.66 + 0.66 + y = 0.997797575 + 0.66 Combine like terms: -0.66 + 0.66 = 0.00 0.00 + y = 0.997797575 + 0.66 y = 0.997797575 + 0.66 Combine like terms: 0.997797575 + 0.66 = 1.657797575 y = 1.657797575 Simplifying y = 1.657797575Subproblem 2
y + -0.66 = -0.997797575 Simplifying y + -0.66 = -0.997797575 Reorder the terms: -0.66 + y = -0.997797575 Solving -0.66 + y = -0.997797575 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.66' to each side of the equation. -0.66 + 0.66 + y = -0.997797575 + 0.66 Combine like terms: -0.66 + 0.66 = 0.00 0.00 + y = -0.997797575 + 0.66 y = -0.997797575 + 0.66 Combine like terms: -0.997797575 + 0.66 = -0.337797575 y = -0.337797575 Simplifying y = -0.337797575Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.657797575, -0.337797575}
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