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Simplifying 36x2 + 288x = 949 Reorder the terms: 288x + 36x2 = 949 Solving 288x + 36x2 = 949 Solving for variable 'x'. Reorder the terms: -949 + 288x + 36x2 = 949 + -949 Combine like terms: 949 + -949 = 0 -949 + 288x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -26.36111111 + 8x + x2 = 0 Move the constant term to the right: Add '26.36111111' to each side of the equation. -26.36111111 + 8x + 26.36111111 + x2 = 0 + 26.36111111 Reorder the terms: -26.36111111 + 26.36111111 + 8x + x2 = 0 + 26.36111111 Combine like terms: -26.36111111 + 26.36111111 = 0.00000000 0.00000000 + 8x + x2 = 0 + 26.36111111 8x + x2 = 0 + 26.36111111 Combine like terms: 0 + 26.36111111 = 26.36111111 8x + x2 = 26.36111111 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 = 26.36111111 + 16 Reorder the terms: 16 + 8x + x2 = 26.36111111 + 16 Combine like terms: 26.36111111 + 16 = 42.36111111 16 + 8x + x2 = 42.36111111 Factor a perfect square on the left side: (x + 4)(x + 4) = 42.36111111 Calculate the square root of the right side: 6.508541397 Break this problem into two subproblems by setting (x + 4) equal to 6.508541397 and -6.508541397.Subproblem 1
x + 4 = 6.508541397 Simplifying x + 4 = 6.508541397 Reorder the terms: 4 + x = 6.508541397 Solving 4 + x = 6.508541397 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 = 6.508541397 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.508541397 + -4 x = 6.508541397 + -4 Combine like terms: 6.508541397 + -4 = 2.508541397 x = 2.508541397 Simplifying x = 2.508541397Subproblem 2
x + 4 = -6.508541397 Simplifying x + 4 = -6.508541397 Reorder the terms: 4 + x = -6.508541397 Solving 4 + x = -6.508541397 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 = -6.508541397 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.508541397 + -4 x = -6.508541397 + -4 Combine like terms: -6.508541397 + -4 = -10.508541397 x = -10.508541397 Simplifying x = -10.508541397Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.508541397, -10.508541397}
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