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Simplifying 5 = -0.24x2 + -2.4x Reorder the terms: 5 = -2.4x + -0.24x2 Solving 5 = -2.4x + -0.24x2 Solving for variable 'x'. Reorder the terms: 5 + 2.4x + 0.24x2 = -2.4x + 2.4x + -0.24x2 + 0.24x2 Combine like terms: -2.4x + 2.4x = 0.0 5 + 2.4x + 0.24x2 = 0.0 + -0.24x2 + 0.24x2 5 + 2.4x + 0.24x2 = -0.24x2 + 0.24x2 Combine like terms: -0.24x2 + 0.24x2 = 0.00 5 + 2.4x + 0.24x2 = 0.00 Begin completing the square. Divide all terms by 0.24 the coefficient of the squared term: Divide each side by '0.24'. 20.83333333 + 10x + x2 = 0 Move the constant term to the right: Add '-20.83333333' to each side of the equation. 20.83333333 + 10x + -20.83333333 + x2 = 0 + -20.83333333 Reorder the terms: 20.83333333 + -20.83333333 + 10x + x2 = 0 + -20.83333333 Combine like terms: 20.83333333 + -20.83333333 = 0.00000000 0.00000000 + 10x + x2 = 0 + -20.83333333 10x + x2 = 0 + -20.83333333 Combine like terms: 0 + -20.83333333 = -20.83333333 10x + x2 = -20.83333333 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -20.83333333 + 25 Reorder the terms: 25 + 10x + x2 = -20.83333333 + 25 Combine like terms: -20.83333333 + 25 = 4.16666667 25 + 10x + x2 = 4.16666667 Factor a perfect square on the left side: (x + 5)(x + 5) = 4.16666667 Calculate the square root of the right side: 2.041241453 Break this problem into two subproblems by setting (x + 5) equal to 2.041241453 and -2.041241453.Subproblem 1
x + 5 = 2.041241453 Simplifying x + 5 = 2.041241453 Reorder the terms: 5 + x = 2.041241453 Solving 5 + x = 2.041241453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 2.041241453 + -5 Combine like terms: 5 + -5 = 0 0 + x = 2.041241453 + -5 x = 2.041241453 + -5 Combine like terms: 2.041241453 + -5 = -2.958758547 x = -2.958758547 Simplifying x = -2.958758547Subproblem 2
x + 5 = -2.041241453 Simplifying x + 5 = -2.041241453 Reorder the terms: 5 + x = -2.041241453 Solving 5 + x = -2.041241453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -2.041241453 + -5 Combine like terms: 5 + -5 = 0 0 + x = -2.041241453 + -5 x = -2.041241453 + -5 Combine like terms: -2.041241453 + -5 = -7.041241453 x = -7.041241453 Simplifying x = -7.041241453Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.958758547, -7.041241453}
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