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Simplifying y2 + 0.4y + -0.05 = 0 Reorder the terms: -0.05 + 0.4y + y2 = 0 Solving -0.05 + 0.4y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '0.05' to each side of the equation. -0.05 + 0.4y + 0.05 + y2 = 0 + 0.05 Reorder the terms: -0.05 + 0.05 + 0.4y + y2 = 0 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + 0.4y + y2 = 0 + 0.05 0.4y + y2 = 0 + 0.05 Combine like terms: 0 + 0.05 = 0.05 0.4y + y2 = 0.05 The y term is 0.4y. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4y + 0.04 + y2 = 0.05 + 0.04 Reorder the terms: 0.04 + 0.4y + y2 = 0.05 + 0.04 Combine like terms: 0.05 + 0.04 = 0.09 0.04 + 0.4y + y2 = 0.09 Factor a perfect square on the left side: (y + 0.2)(y + 0.2) = 0.09 Calculate the square root of the right side: 0.3 Break this problem into two subproblems by setting (y + 0.2) equal to 0.3 and -0.3.Subproblem 1
y + 0.2 = 0.3 Simplifying y + 0.2 = 0.3 Reorder the terms: 0.2 + y = 0.3 Solving 0.2 + y = 0.3 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + y = 0.3 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + y = 0.3 + -0.2 y = 0.3 + -0.2 Combine like terms: 0.3 + -0.2 = 0.1 y = 0.1 Simplifying y = 0.1Subproblem 2
y + 0.2 = -0.3 Simplifying y + 0.2 = -0.3 Reorder the terms: 0.2 + y = -0.3 Solving 0.2 + y = -0.3 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + y = -0.3 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + y = -0.3 + -0.2 y = -0.3 + -0.2 Combine like terms: -0.3 + -0.2 = -0.5 y = -0.5 Simplifying y = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.1, -0.5}
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