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Simplifying 2.4x2 + -10x + -260 = 2x Reorder the terms: -260 + -10x + 2.4x2 = 2x Solving -260 + -10x + 2.4x2 = 2x Solving for variable 'x'. Reorder the terms: -260 + -10x + -2x + 2.4x2 = 2x + -2x Combine like terms: -10x + -2x = -12x -260 + -12x + 2.4x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -260 + -12x + 2.4x2 = 0 Begin completing the square. Divide all terms by 2.4 the coefficient of the squared term: Divide each side by '2.4'. -108.3333333 + -5x + x2 = 0 Move the constant term to the right: Add '108.3333333' to each side of the equation. -108.3333333 + -5x + 108.3333333 + x2 = 0 + 108.3333333 Reorder the terms: -108.3333333 + 108.3333333 + -5x + x2 = 0 + 108.3333333 Combine like terms: -108.3333333 + 108.3333333 = 0.0000000 0.0000000 + -5x + x2 = 0 + 108.3333333 -5x + x2 = 0 + 108.3333333 Combine like terms: 0 + 108.3333333 = 108.3333333 -5x + x2 = 108.3333333 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 108.3333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 108.3333333 + 6.25 Combine like terms: 108.3333333 + 6.25 = 114.5833333 6.25 + -5x + x2 = 114.5833333 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 114.5833333 Calculate the square root of the right side: 10.704360481 Break this problem into two subproblems by setting (x + -2.5) equal to 10.704360481 and -10.704360481.Subproblem 1
x + -2.5 = 10.704360481 Simplifying x + -2.5 = 10.704360481 Reorder the terms: -2.5 + x = 10.704360481 Solving -2.5 + x = 10.704360481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 10.704360481 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 10.704360481 + 2.5 x = 10.704360481 + 2.5 Combine like terms: 10.704360481 + 2.5 = 13.204360481 x = 13.204360481 Simplifying x = 13.204360481Subproblem 2
x + -2.5 = -10.704360481 Simplifying x + -2.5 = -10.704360481 Reorder the terms: -2.5 + x = -10.704360481 Solving -2.5 + x = -10.704360481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -10.704360481 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -10.704360481 + 2.5 x = -10.704360481 + 2.5 Combine like terms: -10.704360481 + 2.5 = -8.204360481 x = -8.204360481 Simplifying x = -8.204360481Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.204360481, -8.204360481}
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