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Simplifying 3x2 + 24x = 7 Reorder the terms: 24x + 3x2 = 7 Solving 24x + 3x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 24x + 3x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + 8x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 8x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 8x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 8x + x2 = 0 + 2.333333333 8x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 8x + x2 = 2.333333333 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 = 2.333333333 + 16 Reorder the terms: 16 + 8x + x2 = 2.333333333 + 16 Combine like terms: 2.333333333 + 16 = 18.333333333 16 + 8x + x2 = 18.333333333 Factor a perfect square on the left side: (x + 4)(x + 4) = 18.333333333 Calculate the square root of the right side: 4.281744193 Break this problem into two subproblems by setting (x + 4) equal to 4.281744193 and -4.281744193.Subproblem 1
x + 4 = 4.281744193 Simplifying x + 4 = 4.281744193 Reorder the terms: 4 + x = 4.281744193 Solving 4 + x = 4.281744193 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 = 4.281744193 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.281744193 + -4 x = 4.281744193 + -4 Combine like terms: 4.281744193 + -4 = 0.281744193 x = 0.281744193 Simplifying x = 0.281744193Subproblem 2
x + 4 = -4.281744193 Simplifying x + 4 = -4.281744193 Reorder the terms: 4 + x = -4.281744193 Solving 4 + x = -4.281744193 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 = -4.281744193 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.281744193 + -4 x = -4.281744193 + -4 Combine like terms: -4.281744193 + -4 = -8.281744193 x = -8.281744193 Simplifying x = -8.281744193Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.281744193, -8.281744193}
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