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Simplifying 3x2 + 24x + 34 = 6 Reorder the terms: 34 + 24x + 3x2 = 6 Solving 34 + 24x + 3x2 = 6 Solving for variable 'x'. Reorder the terms: 34 + -6 + 24x + 3x2 = 6 + -6 Combine like terms: 34 + -6 = 28 28 + 24x + 3x2 = 6 + -6 Combine like terms: 6 + -6 = 0 28 + 24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 9.333333333 + 8x + x2 = 0 Move the constant term to the right: Add '-9.333333333' to each side of the equation. 9.333333333 + 8x + -9.333333333 + x2 = 0 + -9.333333333 Reorder the terms: 9.333333333 + -9.333333333 + 8x + x2 = 0 + -9.333333333 Combine like terms: 9.333333333 + -9.333333333 = 0.000000000 0.000000000 + 8x + x2 = 0 + -9.333333333 8x + x2 = 0 + -9.333333333 Combine like terms: 0 + -9.333333333 = -9.333333333 8x + x2 = -9.333333333 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -9.333333333 + 16 Reorder the terms: 16 + 8x + x2 = -9.333333333 + 16 Combine like terms: -9.333333333 + 16 = 6.666666667 16 + 8x + x2 = 6.666666667 Factor a perfect square on the left side: (x + 4)(x + 4) = 6.666666667 Calculate the square root of the right side: 2.581988898 Break this problem into two subproblems by setting (x + 4) equal to 2.581988898 and -2.581988898.Subproblem 1
x + 4 = 2.581988898 Simplifying x + 4 = 2.581988898 Reorder the terms: 4 + x = 2.581988898 Solving 4 + x = 2.581988898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 2.581988898 + -4 Combine like terms: 4 + -4 = 0 0 + x = 2.581988898 + -4 x = 2.581988898 + -4 Combine like terms: 2.581988898 + -4 = -1.418011102 x = -1.418011102 Simplifying x = -1.418011102Subproblem 2
x + 4 = -2.581988898 Simplifying x + 4 = -2.581988898 Reorder the terms: 4 + x = -2.581988898 Solving 4 + x = -2.581988898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -2.581988898 + -4 Combine like terms: 4 + -4 = 0 0 + x = -2.581988898 + -4 x = -2.581988898 + -4 Combine like terms: -2.581988898 + -4 = -6.581988898 x = -6.581988898 Simplifying x = -6.581988898Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.418011102, -6.581988898}
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