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Simplifying 48x2 + -24x + -13 = 0 Reorder the terms: -13 + -24x + 48x2 = 0 Solving -13 + -24x + 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 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.2708333333' to each side of the equation. -0.2708333333 + -0.5x + 0.2708333333 + x2 = 0 + 0.2708333333 Reorder the terms: -0.2708333333 + 0.2708333333 + -0.5x + x2 = 0 + 0.2708333333 Combine like terms: -0.2708333333 + 0.2708333333 = 0.0000000000 0.0000000000 + -0.5x + x2 = 0 + 0.2708333333 -0.5x + x2 = 0 + 0.2708333333 Combine like terms: 0 + 0.2708333333 = 0.2708333333 -0.5x + x2 = 0.2708333333 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.2708333333 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.2708333333 + 0.0625 Combine like terms: 0.2708333333 + 0.0625 = 0.3333333333 0.0625 + -0.5x + x2 = 0.3333333333 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.3333333333 Calculate the square root of the right side: 0.577350269 Break this problem into two subproblems by setting (x + -0.25) equal to 0.577350269 and -0.577350269.Subproblem 1
x + -0.25 = 0.577350269 Simplifying x + -0.25 = 0.577350269 Reorder the terms: -0.25 + x = 0.577350269 Solving -0.25 + x = 0.577350269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.577350269 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.577350269 + 0.25 x = 0.577350269 + 0.25 Combine like terms: 0.577350269 + 0.25 = 0.827350269 x = 0.827350269 Simplifying x = 0.827350269Subproblem 2
x + -0.25 = -0.577350269 Simplifying x + -0.25 = -0.577350269 Reorder the terms: -0.25 + x = -0.577350269 Solving -0.25 + x = -0.577350269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.577350269 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.577350269 + 0.25 x = -0.577350269 + 0.25 Combine like terms: -0.577350269 + 0.25 = -0.327350269 x = -0.327350269 Simplifying x = -0.327350269Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.827350269, -0.327350269}
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