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Simplifying y2 + -0.6y + 0.08 = 0 Reorder the terms: 0.08 + -0.6y + y2 = 0 Solving 0.08 + -0.6y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-0.08' to each side of the equation. 0.08 + -0.6y + -0.08 + y2 = 0 + -0.08 Reorder the terms: 0.08 + -0.08 + -0.6y + y2 = 0 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + -0.6y + y2 = 0 + -0.08 -0.6y + y2 = 0 + -0.08 Combine like terms: 0 + -0.08 = -0.08 -0.6y + y2 = -0.08 The y term is -0.6y. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6y + 0.09 + y2 = -0.08 + 0.09 Reorder the terms: 0.09 + -0.6y + y2 = -0.08 + 0.09 Combine like terms: -0.08 + 0.09 = 0.01 0.09 + -0.6y + y2 = 0.01 Factor a perfect square on the left side: (y + -0.3)(y + -0.3) = 0.01 Calculate the square root of the right side: 0.1 Break this problem into two subproblems by setting (y + -0.3) equal to 0.1 and -0.1.Subproblem 1
y + -0.3 = 0.1 Simplifying y + -0.3 = 0.1 Reorder the terms: -0.3 + y = 0.1 Solving -0.3 + y = 0.1 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + y = 0.1 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + y = 0.1 + 0.3 y = 0.1 + 0.3 Combine like terms: 0.1 + 0.3 = 0.4 y = 0.4 Simplifying y = 0.4Subproblem 2
y + -0.3 = -0.1 Simplifying y + -0.3 = -0.1 Reorder the terms: -0.3 + y = -0.1 Solving -0.3 + y = -0.1 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + y = -0.1 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + y = -0.1 + 0.3 y = -0.1 + 0.3 Combine like terms: -0.1 + 0.3 = 0.2 y = 0.2 Simplifying y = 0.2Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.4, 0.2}
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