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Simplifying 3x2 + 24x = 52 Reorder the terms: 24x + 3x2 = 52 Solving 24x + 3x2 = 52 Solving for variable 'x'. Reorder the terms: -52 + 24x + 3x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + 24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -17.33333333 + 8x + x2 = 0 Move the constant term to the right: Add '17.33333333' to each side of the equation. -17.33333333 + 8x + 17.33333333 + x2 = 0 + 17.33333333 Reorder the terms: -17.33333333 + 17.33333333 + 8x + x2 = 0 + 17.33333333 Combine like terms: -17.33333333 + 17.33333333 = 0.00000000 0.00000000 + 8x + x2 = 0 + 17.33333333 8x + x2 = 0 + 17.33333333 Combine like terms: 0 + 17.33333333 = 17.33333333 8x + x2 = 17.33333333 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 = 17.33333333 + 16 Reorder the terms: 16 + 8x + x2 = 17.33333333 + 16 Combine like terms: 17.33333333 + 16 = 33.33333333 16 + 8x + x2 = 33.33333333 Factor a perfect square on the left side: (x + 4)(x + 4) = 33.33333333 Calculate the square root of the right side: 5.773502692 Break this problem into two subproblems by setting (x + 4) equal to 5.773502692 and -5.773502692.Subproblem 1
x + 4 = 5.773502692 Simplifying x + 4 = 5.773502692 Reorder the terms: 4 + x = 5.773502692 Solving 4 + x = 5.773502692 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 = 5.773502692 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.773502692 + -4 x = 5.773502692 + -4 Combine like terms: 5.773502692 + -4 = 1.773502692 x = 1.773502692 Simplifying x = 1.773502692Subproblem 2
x + 4 = -5.773502692 Simplifying x + 4 = -5.773502692 Reorder the terms: 4 + x = -5.773502692 Solving 4 + x = -5.773502692 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 = -5.773502692 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.773502692 + -4 x = -5.773502692 + -4 Combine like terms: -5.773502692 + -4 = -9.773502692 x = -9.773502692 Simplifying x = -9.773502692Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.773502692, -9.773502692}
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