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Simplifying y2 + -1.25y + 0.390625 = 0 Reorder the terms: 0.390625 + -1.25y + y2 = 0 Solving 0.390625 + -1.25y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-0.390625' to each side of the equation. 0.390625 + -1.25y + -0.390625 + y2 = 0 + -0.390625 Reorder the terms: 0.390625 + -0.390625 + -1.25y + y2 = 0 + -0.390625 Combine like terms: 0.390625 + -0.390625 = 0.000000 0.000000 + -1.25y + y2 = 0 + -0.390625 -1.25y + y2 = 0 + -0.390625 Combine like terms: 0 + -0.390625 = -0.390625 -1.25y + y2 = -0.390625 The y term is -1.25y. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25y + 0.390625 + y2 = -0.390625 + 0.390625 Reorder the terms: 0.390625 + -1.25y + y2 = -0.390625 + 0.390625 Combine like terms: -0.390625 + 0.390625 = 0.000000 0.390625 + -1.25y + y2 = 0.000000 Factor a perfect square on the left side: (y + -0.625)(y + -0.625) = 0.000000 Calculate the square root of the right side: 0.000000 Break this problem into two subproblems by setting (y + -0.625) equal to 0.000000 and 0.000000.Subproblem 1
y + -0.625 = 0.000000 Simplifying y + -0.625 = 0.000000 Reorder the terms: -0.625 + y = 0.000000 Solving -0.625 + y = 0.000000 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + y = 0.000000 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + y = 0.000000 + 0.625 y = 0.000000 + 0.625 Combine like terms: 0.000000 + 0.625 = 0.625 y = 0.625 Simplifying y = 0.625Subproblem 2
y + -0.625 = 0.000000 Simplifying y + -0.625 = 0.000000 Reorder the terms: -0.625 + y = 0.000000 Solving -0.625 + y = 0.000000 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + y = 0.000000 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + y = 0.000000 + 0.625 y = 0.000000 + 0.625 Combine like terms: 0.000000 + 0.625 = 0.625 y = 0.625 Simplifying y = 0.625Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.625, 0.625}
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