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Simplifying 6x2 + 24x + 13 = 0 Reorder the terms: 13 + 24x + 6x2 = 0 Solving 13 + 24x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.166666667 + 4x + x2 = 0 Move the constant term to the right: Add '-2.166666667' to each side of the equation. 2.166666667 + 4x + -2.166666667 + x2 = 0 + -2.166666667 Reorder the terms: 2.166666667 + -2.166666667 + 4x + x2 = 0 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + 4x + x2 = 0 + -2.166666667 4x + x2 = 0 + -2.166666667 Combine like terms: 0 + -2.166666667 = -2.166666667 4x + x2 = -2.166666667 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 = -2.166666667 + 4 Reorder the terms: 4 + 4x + x2 = -2.166666667 + 4 Combine like terms: -2.166666667 + 4 = 1.833333333 4 + 4x + x2 = 1.833333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 1.833333333 Calculate the square root of the right side: 1.354006401 Break this problem into two subproblems by setting (x + 2) equal to 1.354006401 and -1.354006401.Subproblem 1
x + 2 = 1.354006401 Simplifying x + 2 = 1.354006401 Reorder the terms: 2 + x = 1.354006401 Solving 2 + x = 1.354006401 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 = 1.354006401 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.354006401 + -2 x = 1.354006401 + -2 Combine like terms: 1.354006401 + -2 = -0.645993599 x = -0.645993599 Simplifying x = -0.645993599Subproblem 2
x + 2 = -1.354006401 Simplifying x + 2 = -1.354006401 Reorder the terms: 2 + x = -1.354006401 Solving 2 + x = -1.354006401 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 = -1.354006401 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.354006401 + -2 x = -1.354006401 + -2 Combine like terms: -1.354006401 + -2 = -3.354006401 x = -3.354006401 Simplifying x = -3.354006401Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.645993599, -3.354006401}
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