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Simplifying 5y2 + -1y + -0.5 = 0 Reorder the terms: -0.5 + -1y + 5y2 = 0 Solving -0.5 + -1y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.1 + -0.2y + y2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -0.2y + 0.1 + y2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + -0.2y + y2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -0.2y + y2 = 0 + 0.1 -0.2y + y2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 -0.2y + y2 = 0.1 The y term is -0.2y. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2y + 0.01 + y2 = 0.1 + 0.01 Reorder the terms: 0.01 + -0.2y + y2 = 0.1 + 0.01 Combine like terms: 0.1 + 0.01 = 0.11 0.01 + -0.2y + y2 = 0.11 Factor a perfect square on the left side: (y + -0.1)(y + -0.1) = 0.11 Calculate the square root of the right side: 0.331662479 Break this problem into two subproblems by setting (y + -0.1) equal to 0.331662479 and -0.331662479.Subproblem 1
y + -0.1 = 0.331662479 Simplifying y + -0.1 = 0.331662479 Reorder the terms: -0.1 + y = 0.331662479 Solving -0.1 + y = 0.331662479 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + y = 0.331662479 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + y = 0.331662479 + 0.1 y = 0.331662479 + 0.1 Combine like terms: 0.331662479 + 0.1 = 0.431662479 y = 0.431662479 Simplifying y = 0.431662479Subproblem 2
y + -0.1 = -0.331662479 Simplifying y + -0.1 = -0.331662479 Reorder the terms: -0.1 + y = -0.331662479 Solving -0.1 + y = -0.331662479 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + y = -0.331662479 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + y = -0.331662479 + 0.1 y = -0.331662479 + 0.1 Combine like terms: -0.331662479 + 0.1 = -0.231662479 y = -0.231662479 Simplifying y = -0.231662479Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.431662479, -0.231662479}
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