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Simplifying 200 = 2 * 3.14X2 + 2 * 3.14X * 6 Multiply 2 * 3.14 200 = 6.28X2 + 2 * 3.14X * 6 Reorder the terms for easier multiplication: 200 = 6.28X2 + 2 * 3.14 * 6X Multiply 2 * 3.14 200 = 6.28X2 + 6.28 * 6X Multiply 6.28 * 6 200 = 6.28X2 + 37.68X Reorder the terms: 200 = 37.68X + 6.28X2 Solving 200 = 37.68X + 6.28X2 Solving for variable 'X'. Reorder the terms: 200 + -37.68X + -6.28X2 = 37.68X + -37.68X + 6.28X2 + -6.28X2 Combine like terms: 37.68X + -37.68X = 0.00 200 + -37.68X + -6.28X2 = 0.00 + 6.28X2 + -6.28X2 200 + -37.68X + -6.28X2 = 6.28X2 + -6.28X2 Combine like terms: 6.28X2 + -6.28X2 = 0.00 200 + -37.68X + -6.28X2 = 0.00 Begin completing the square. Divide all terms by -6.28 the coefficient of the squared term: Divide each side by '-6.28'. -31.84713376 + 6X + X2 = 0 Move the constant term to the right: Add '31.84713376' to each side of the equation. -31.84713376 + 6X + 31.84713376 + X2 = 0 + 31.84713376 Reorder the terms: -31.84713376 + 31.84713376 + 6X + X2 = 0 + 31.84713376 Combine like terms: -31.84713376 + 31.84713376 = 0.00000000 0.00000000 + 6X + X2 = 0 + 31.84713376 6X + X2 = 0 + 31.84713376 Combine like terms: 0 + 31.84713376 = 31.84713376 6X + X2 = 31.84713376 The X term is 6X. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6X + 9 + X2 = 31.84713376 + 9 Reorder the terms: 9 + 6X + X2 = 31.84713376 + 9 Combine like terms: 31.84713376 + 9 = 40.84713376 9 + 6X + X2 = 40.84713376 Factor a perfect square on the left side: (X + 3)(X + 3) = 40.84713376 Calculate the square root of the right side: 6.391176242 Break this problem into two subproblems by setting (X + 3) equal to 6.391176242 and -6.391176242.Subproblem 1
X + 3 = 6.391176242 Simplifying X + 3 = 6.391176242 Reorder the terms: 3 + X = 6.391176242 Solving 3 + X = 6.391176242 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + X = 6.391176242 + -3 Combine like terms: 3 + -3 = 0 0 + X = 6.391176242 + -3 X = 6.391176242 + -3 Combine like terms: 6.391176242 + -3 = 3.391176242 X = 3.391176242 Simplifying X = 3.391176242Subproblem 2
X + 3 = -6.391176242 Simplifying X + 3 = -6.391176242 Reorder the terms: 3 + X = -6.391176242 Solving 3 + X = -6.391176242 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + X = -6.391176242 + -3 Combine like terms: 3 + -3 = 0 0 + X = -6.391176242 + -3 X = -6.391176242 + -3 Combine like terms: -6.391176242 + -3 = -9.391176242 X = -9.391176242 Simplifying X = -9.391176242Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.391176242, -9.391176242}
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