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Simplifying 48x2 + 48x + -13 = 0 Reorder the terms: -13 + 48x + 48x2 = 0 Solving -13 + 48x + 48x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.2708333333 + x + x2 = 0 Move the constant term to the right: Add '0.2708333333' to each side of the equation. -0.2708333333 + x + 0.2708333333 + x2 = 0 + 0.2708333333 Reorder the terms: -0.2708333333 + 0.2708333333 + x + x2 = 0 + 0.2708333333 Combine like terms: -0.2708333333 + 0.2708333333 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.2708333333 x + x2 = 0 + 0.2708333333 Combine like terms: 0 + 0.2708333333 = 0.2708333333 x + x2 = 0.2708333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.2708333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.2708333333 + 0.25 Combine like terms: 0.2708333333 + 0.25 = 0.5208333333 1.25 + x2 = 0.5208333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.5208333333 Calculate the square root of the right side: 0.721687836 Break this problem into two subproblems by setting (x + 0.5) equal to 0.721687836 and -0.721687836.Subproblem 1
x + 0.5 = 0.721687836 Simplifying x + 0.5 = 0.721687836 Reorder the terms: 0.5 + x = 0.721687836 Solving 0.5 + x = 0.721687836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.721687836 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.721687836 + -0.5 x = 0.721687836 + -0.5 Combine like terms: 0.721687836 + -0.5 = 0.221687836 x = 0.221687836 Simplifying x = 0.221687836Subproblem 2
x + 0.5 = -0.721687836 Simplifying x + 0.5 = -0.721687836 Reorder the terms: 0.5 + x = -0.721687836 Solving 0.5 + x = -0.721687836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.721687836 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.721687836 + -0.5 x = -0.721687836 + -0.5 Combine like terms: -0.721687836 + -0.5 = -1.221687836 x = -1.221687836 Simplifying x = -1.221687836Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.221687836, -1.221687836}
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