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Simplifying 2y(5y + -1) = 13 Reorder the terms: 2y(-1 + 5y) = 13 (-1 * 2y + 5y * 2y) = 13 (-2y + 10y2) = 13 Solving -2y + 10y2 = 13 Solving for variable 'y'. Reorder the terms: -13 + -2y + 10y2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -2y + 10y2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.3 + -0.2y + y2 = 0.0 Move the constant term to the right: Add '1.3' to each side of the equation. -1.3 + -0.2y + 1.3 + y2 = 0.0 + 1.3 Reorder the terms: -1.3 + 1.3 + -0.2y + y2 = 0.0 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + -0.2y + y2 = 0.0 + 1.3 -0.2y + y2 = 0.0 + 1.3 Combine like terms: 0.0 + 1.3 = 1.3 -0.2y + y2 = 1.3 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 = 1.3 + 0.01 Reorder the terms: 0.01 + -0.2y + y2 = 1.3 + 0.01 Combine like terms: 1.3 + 0.01 = 1.31 0.01 + -0.2y + y2 = 1.31 Factor a perfect square on the left side: (y + -0.1)(y + -0.1) = 1.31 Calculate the square root of the right side: 1.144552314 Break this problem into two subproblems by setting (y + -0.1) equal to 1.144552314 and -1.144552314.Subproblem 1
y + -0.1 = 1.144552314 Simplifying y + -0.1 = 1.144552314 Reorder the terms: -0.1 + y = 1.144552314 Solving -0.1 + y = 1.144552314 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 = 1.144552314 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + y = 1.144552314 + 0.1 y = 1.144552314 + 0.1 Combine like terms: 1.144552314 + 0.1 = 1.244552314 y = 1.244552314 Simplifying y = 1.244552314Subproblem 2
y + -0.1 = -1.144552314 Simplifying y + -0.1 = -1.144552314 Reorder the terms: -0.1 + y = -1.144552314 Solving -0.1 + y = -1.144552314 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 = -1.144552314 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + y = -1.144552314 + 0.1 y = -1.144552314 + 0.1 Combine like terms: -1.144552314 + 0.1 = -1.044552314 y = -1.044552314 Simplifying y = -1.044552314Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.244552314, -1.044552314}
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