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Simplifying 320y2 + -605y + 279 = 0 Reorder the terms: 279 + -605y + 320y2 = 0 Solving 279 + -605y + 320y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 320 the coefficient of the squared term: Divide each side by '320'. 0.871875 + -1.890625y + y2 = 0 Move the constant term to the right: Add '-0.871875' to each side of the equation. 0.871875 + -1.890625y + -0.871875 + y2 = 0 + -0.871875 Reorder the terms: 0.871875 + -0.871875 + -1.890625y + y2 = 0 + -0.871875 Combine like terms: 0.871875 + -0.871875 = 0.000000 0.000000 + -1.890625y + y2 = 0 + -0.871875 -1.890625y + y2 = 0 + -0.871875 Combine like terms: 0 + -0.871875 = -0.871875 -1.890625y + y2 = -0.871875 The y term is -1.890625y. Take half its coefficient (-0.9453125). Square it (0.8936157227) and add it to both sides. Add '0.8936157227' to each side of the equation. -1.890625y + 0.8936157227 + y2 = -0.871875 + 0.8936157227 Reorder the terms: 0.8936157227 + -1.890625y + y2 = -0.871875 + 0.8936157227 Combine like terms: -0.871875 + 0.8936157227 = 0.0217407227 0.8936157227 + -1.890625y + y2 = 0.0217407227 Factor a perfect square on the left side: (y + -0.9453125)(y + -0.9453125) = 0.0217407227 Calculate the square root of the right side: 0.147447356 Break this problem into two subproblems by setting (y + -0.9453125) equal to 0.147447356 and -0.147447356.Subproblem 1
y + -0.9453125 = 0.147447356 Simplifying y + -0.9453125 = 0.147447356 Reorder the terms: -0.9453125 + y = 0.147447356 Solving -0.9453125 + y = 0.147447356 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.9453125' to each side of the equation. -0.9453125 + 0.9453125 + y = 0.147447356 + 0.9453125 Combine like terms: -0.9453125 + 0.9453125 = 0.0000000 0.0000000 + y = 0.147447356 + 0.9453125 y = 0.147447356 + 0.9453125 Combine like terms: 0.147447356 + 0.9453125 = 1.092759856 y = 1.092759856 Simplifying y = 1.092759856Subproblem 2
y + -0.9453125 = -0.147447356 Simplifying y + -0.9453125 = -0.147447356 Reorder the terms: -0.9453125 + y = -0.147447356 Solving -0.9453125 + y = -0.147447356 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.9453125' to each side of the equation. -0.9453125 + 0.9453125 + y = -0.147447356 + 0.9453125 Combine like terms: -0.9453125 + 0.9453125 = 0.0000000 0.0000000 + y = -0.147447356 + 0.9453125 y = -0.147447356 + 0.9453125 Combine like terms: -0.147447356 + 0.9453125 = 0.797865144 y = 0.797865144 Simplifying y = 0.797865144Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.092759856, 0.797865144}
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