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Simplifying (5y2 + -2y + -1) = 0 Reorder the terms: (-1 + -2y + 5y2) = 0 Remove parenthesis around (-1 + -2y + 5y2) -1 + -2y + 5y2 = 0 Solving -1 + -2y + 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'. -0.2 + -0.4y + y2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.4y + 0.2 + y2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.4y + y2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.4y + y2 = 0 + 0.2 -0.4y + y2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.4y + y2 = 0.2 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 = 0.2 + 0.04 Reorder the terms: 0.04 + -0.4y + y2 = 0.2 + 0.04 Combine like terms: 0.2 + 0.04 = 0.24 0.04 + -0.4y + y2 = 0.24 Factor a perfect square on the left side: (y + -0.2)(y + -0.2) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (y + -0.2) equal to 0.489897949 and -0.489897949.Subproblem 1
y + -0.2 = 0.489897949 Simplifying y + -0.2 = 0.489897949 Reorder the terms: -0.2 + y = 0.489897949 Solving -0.2 + y = 0.489897949 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 = 0.489897949 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + y = 0.489897949 + 0.2 y = 0.489897949 + 0.2 Combine like terms: 0.489897949 + 0.2 = 0.689897949 y = 0.689897949 Simplifying y = 0.689897949Subproblem 2
y + -0.2 = -0.489897949 Simplifying y + -0.2 = -0.489897949 Reorder the terms: -0.2 + y = -0.489897949 Solving -0.2 + y = -0.489897949 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 = -0.489897949 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + y = -0.489897949 + 0.2 y = -0.489897949 + 0.2 Combine like terms: -0.489897949 + 0.2 = -0.289897949 y = -0.289897949 Simplifying y = -0.289897949Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.689897949, -0.289897949}
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