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Simplifying 2y2 + 25y + -150 = 0 Reorder the terms: -150 + 25y + 2y2 = 0 Solving -150 + 25y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -75 + 12.5y + y2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + 12.5y + 75 + y2 = 0 + 75 Reorder the terms: -75 + 75 + 12.5y + y2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 12.5y + y2 = 0 + 75 12.5y + y2 = 0 + 75 Combine like terms: 0 + 75 = 75 12.5y + y2 = 75 The y term is 12.5y. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5y + 39.0625 + y2 = 75 + 39.0625 Reorder the terms: 39.0625 + 12.5y + y2 = 75 + 39.0625 Combine like terms: 75 + 39.0625 = 114.0625 39.0625 + 12.5y + y2 = 114.0625 Factor a perfect square on the left side: (y + 6.25)(y + 6.25) = 114.0625 Calculate the square root of the right side: 10.680004682 Break this problem into two subproblems by setting (y + 6.25) equal to 10.680004682 and -10.680004682.Subproblem 1
y + 6.25 = 10.680004682 Simplifying y + 6.25 = 10.680004682 Reorder the terms: 6.25 + y = 10.680004682 Solving 6.25 + y = 10.680004682 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + y = 10.680004682 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + y = 10.680004682 + -6.25 y = 10.680004682 + -6.25 Combine like terms: 10.680004682 + -6.25 = 4.430004682 y = 4.430004682 Simplifying y = 4.430004682Subproblem 2
y + 6.25 = -10.680004682 Simplifying y + 6.25 = -10.680004682 Reorder the terms: 6.25 + y = -10.680004682 Solving 6.25 + y = -10.680004682 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + y = -10.680004682 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + y = -10.680004682 + -6.25 y = -10.680004682 + -6.25 Combine like terms: -10.680004682 + -6.25 = -16.930004682 y = -16.930004682 Simplifying y = -16.930004682Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.430004682, -16.930004682}
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