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Simplifying 3x2 + 24x + 4 = 0 Reorder the terms: 4 + 24x + 3x2 = 0 Solving 4 + 24x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 8x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 8x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 8x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 8x + x2 = 0 + -1.333333333 8x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 8x + x2 = -1.333333333 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 = -1.333333333 + 16 Reorder the terms: 16 + 8x + x2 = -1.333333333 + 16 Combine like terms: -1.333333333 + 16 = 14.666666667 16 + 8x + x2 = 14.666666667 Factor a perfect square on the left side: (x + 4)(x + 4) = 14.666666667 Calculate the square root of the right side: 3.829708431 Break this problem into two subproblems by setting (x + 4) equal to 3.829708431 and -3.829708431.Subproblem 1
x + 4 = 3.829708431 Simplifying x + 4 = 3.829708431 Reorder the terms: 4 + x = 3.829708431 Solving 4 + x = 3.829708431 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 = 3.829708431 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.829708431 + -4 x = 3.829708431 + -4 Combine like terms: 3.829708431 + -4 = -0.170291569 x = -0.170291569 Simplifying x = -0.170291569Subproblem 2
x + 4 = -3.829708431 Simplifying x + 4 = -3.829708431 Reorder the terms: 4 + x = -3.829708431 Solving 4 + x = -3.829708431 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 = -3.829708431 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.829708431 + -4 x = -3.829708431 + -4 Combine like terms: -3.829708431 + -4 = -7.829708431 x = -7.829708431 Simplifying x = -7.829708431Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.170291569, -7.829708431}
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