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Simplifying 4y2 + -100y + 3 = 0 Reorder the terms: 3 + -100y + 4y2 = 0 Solving 3 + -100y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -25y + y2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -25y + -0.75 + y2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -25y + y2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -25y + y2 = 0 + -0.75 -25y + y2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -25y + y2 = -0.75 The y term is -25y. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25y + 156.25 + y2 = -0.75 + 156.25 Reorder the terms: 156.25 + -25y + y2 = -0.75 + 156.25 Combine like terms: -0.75 + 156.25 = 155.5 156.25 + -25y + y2 = 155.5 Factor a perfect square on the left side: (y + -12.5)(y + -12.5) = 155.5 Calculate the square root of the right side: 12.469963913 Break this problem into two subproblems by setting (y + -12.5) equal to 12.469963913 and -12.469963913.Subproblem 1
y + -12.5 = 12.469963913 Simplifying y + -12.5 = 12.469963913 Reorder the terms: -12.5 + y = 12.469963913 Solving -12.5 + y = 12.469963913 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + y = 12.469963913 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + y = 12.469963913 + 12.5 y = 12.469963913 + 12.5 Combine like terms: 12.469963913 + 12.5 = 24.969963913 y = 24.969963913 Simplifying y = 24.969963913Subproblem 2
y + -12.5 = -12.469963913 Simplifying y + -12.5 = -12.469963913 Reorder the terms: -12.5 + y = -12.469963913 Solving -12.5 + y = -12.469963913 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + y = -12.469963913 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + y = -12.469963913 + 12.5 y = -12.469963913 + 12.5 Combine like terms: -12.469963913 + 12.5 = 0.030036087 y = 0.030036087 Simplifying y = 0.030036087Solution
The solution to the problem is based on the solutions from the subproblems. y = {24.969963913, 0.030036087}
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