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Simplifying 7x2 + 2x = 3600 Reorder the terms: 2x + 7x2 = 3600 Solving 2x + 7x2 = 3600 Solving for variable 'x'. Reorder the terms: -3600 + 2x + 7x2 = 3600 + -3600 Combine like terms: 3600 + -3600 = 0 -3600 + 2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -514.2857143 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '514.2857143' to each side of the equation. -514.2857143 + 0.2857142857x + 514.2857143 + x2 = 0 + 514.2857143 Reorder the terms: -514.2857143 + 514.2857143 + 0.2857142857x + x2 = 0 + 514.2857143 Combine like terms: -514.2857143 + 514.2857143 = 0.0000000 0.0000000 + 0.2857142857x + x2 = 0 + 514.2857143 0.2857142857x + x2 = 0 + 514.2857143 Combine like terms: 0 + 514.2857143 = 514.2857143 0.2857142857x + x2 = 514.2857143 The x term is 0.2857142857x. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857x + 0.02040816328 + x2 = 514.2857143 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 514.2857143 + 0.02040816328 Combine like terms: 514.2857143 + 0.02040816328 = 514.30612246328 0.02040816328 + 0.2857142857x + x2 = 514.30612246328 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 514.30612246328 Calculate the square root of the right side: 22.678318334 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 22.678318334 and -22.678318334.Subproblem 1
x + 0.1428571429 = 22.678318334 Simplifying x + 0.1428571429 = 22.678318334 Reorder the terms: 0.1428571429 + x = 22.678318334 Solving 0.1428571429 + x = 22.678318334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = 22.678318334 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 22.678318334 + -0.1428571429 x = 22.678318334 + -0.1428571429 Combine like terms: 22.678318334 + -0.1428571429 = 22.5354611911 x = 22.5354611911 Simplifying x = 22.5354611911Subproblem 2
x + 0.1428571429 = -22.678318334 Simplifying x + 0.1428571429 = -22.678318334 Reorder the terms: 0.1428571429 + x = -22.678318334 Solving 0.1428571429 + x = -22.678318334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = -22.678318334 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -22.678318334 + -0.1428571429 x = -22.678318334 + -0.1428571429 Combine like terms: -22.678318334 + -0.1428571429 = -22.8211754769 x = -22.8211754769 Simplifying x = -22.8211754769Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.5354611911, -22.8211754769}
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