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Simplifying 6x2 + 24x = -0.2 Reorder the terms: 24x + 6x2 = -0.2 Solving 24x + 6x2 = -0.2 Solving for variable 'x'. Reorder the terms: 0.2 + 24x + 6x2 = -0.2 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.2 + 24x + 6x2 = 0.0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.03333333333 + 4x + x2 = 0.0 Move the constant term to the right: Add '-0.03333333333' to each side of the equation. 0.03333333333 + 4x + -0.03333333333 + x2 = 0.0 + -0.03333333333 Reorder the terms: 0.03333333333 + -0.03333333333 + 4x + x2 = 0.0 + -0.03333333333 Combine like terms: 0.03333333333 + -0.03333333333 = 0.00000000000 0.00000000000 + 4x + x2 = 0.0 + -0.03333333333 4x + x2 = 0.0 + -0.03333333333 Combine like terms: 0.0 + -0.03333333333 = -0.03333333333 4x + x2 = -0.03333333333 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -0.03333333333 + 4 Reorder the terms: 4 + 4x + x2 = -0.03333333333 + 4 Combine like terms: -0.03333333333 + 4 = 3.96666666667 4 + 4x + x2 = 3.96666666667 Factor a perfect square on the left side: (x + 2)(x + 2) = 3.96666666667 Calculate the square root of the right side: 1.991649233 Break this problem into two subproblems by setting (x + 2) equal to 1.991649233 and -1.991649233.Subproblem 1
x + 2 = 1.991649233 Simplifying x + 2 = 1.991649233 Reorder the terms: 2 + x = 1.991649233 Solving 2 + x = 1.991649233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.991649233 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.991649233 + -2 x = 1.991649233 + -2 Combine like terms: 1.991649233 + -2 = -0.008350767 x = -0.008350767 Simplifying x = -0.008350767Subproblem 2
x + 2 = -1.991649233 Simplifying x + 2 = -1.991649233 Reorder the terms: 2 + x = -1.991649233 Solving 2 + x = -1.991649233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.991649233 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.991649233 + -2 x = -1.991649233 + -2 Combine like terms: -1.991649233 + -2 = -3.991649233 x = -3.991649233 Simplifying x = -3.991649233Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.008350767, -3.991649233}
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