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Simplifying 3x2 + 24x = 71 Reorder the terms: 24x + 3x2 = 71 Solving 24x + 3x2 = 71 Solving for variable 'x'. Reorder the terms: -71 + 24x + 3x2 = 71 + -71 Combine like terms: 71 + -71 = 0 -71 + 24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -23.66666667 + 8x + x2 = 0 Move the constant term to the right: Add '23.66666667' to each side of the equation. -23.66666667 + 8x + 23.66666667 + x2 = 0 + 23.66666667 Reorder the terms: -23.66666667 + 23.66666667 + 8x + x2 = 0 + 23.66666667 Combine like terms: -23.66666667 + 23.66666667 = 0.00000000 0.00000000 + 8x + x2 = 0 + 23.66666667 8x + x2 = 0 + 23.66666667 Combine like terms: 0 + 23.66666667 = 23.66666667 8x + x2 = 23.66666667 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 = 23.66666667 + 16 Reorder the terms: 16 + 8x + x2 = 23.66666667 + 16 Combine like terms: 23.66666667 + 16 = 39.66666667 16 + 8x + x2 = 39.66666667 Factor a perfect square on the left side: (x + 4)(x + 4) = 39.66666667 Calculate the square root of the right side: 6.298147876 Break this problem into two subproblems by setting (x + 4) equal to 6.298147876 and -6.298147876.Subproblem 1
x + 4 = 6.298147876 Simplifying x + 4 = 6.298147876 Reorder the terms: 4 + x = 6.298147876 Solving 4 + x = 6.298147876 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 = 6.298147876 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.298147876 + -4 x = 6.298147876 + -4 Combine like terms: 6.298147876 + -4 = 2.298147876 x = 2.298147876 Simplifying x = 2.298147876Subproblem 2
x + 4 = -6.298147876 Simplifying x + 4 = -6.298147876 Reorder the terms: 4 + x = -6.298147876 Solving 4 + x = -6.298147876 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 = -6.298147876 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.298147876 + -4 x = -6.298147876 + -4 Combine like terms: -6.298147876 + -4 = -10.298147876 x = -10.298147876 Simplifying x = -10.298147876Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.298147876, -10.298147876}
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