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Simplifying 2x2 + 84x + -5544 = 0 Reorder the terms: -5544 + 84x + 2x2 = 0 Solving -5544 + 84x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2772 + 42x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2772 + 42x + x2)' equal to zero and attempt to solve: Simplifying -2772 + 42x + x2 = 0 Solving -2772 + 42x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2772' to each side of the equation. -2772 + 42x + 2772 + x2 = 0 + 2772 Reorder the terms: -2772 + 2772 + 42x + x2 = 0 + 2772 Combine like terms: -2772 + 2772 = 0 0 + 42x + x2 = 0 + 2772 42x + x2 = 0 + 2772 Combine like terms: 0 + 2772 = 2772 42x + x2 = 2772 The x term is 42x. Take half its coefficient (21). Square it (441) and add it to both sides. Add '441' to each side of the equation. 42x + 441 + x2 = 2772 + 441 Reorder the terms: 441 + 42x + x2 = 2772 + 441 Combine like terms: 2772 + 441 = 3213 441 + 42x + x2 = 3213 Factor a perfect square on the left side: (x + 21)(x + 21) = 3213 Calculate the square root of the right side: 56.683330883 Break this problem into two subproblems by setting (x + 21) equal to 56.683330883 and -56.683330883.Subproblem 1
x + 21 = 56.683330883 Simplifying x + 21 = 56.683330883 Reorder the terms: 21 + x = 56.683330883 Solving 21 + x = 56.683330883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = 56.683330883 + -21 Combine like terms: 21 + -21 = 0 0 + x = 56.683330883 + -21 x = 56.683330883 + -21 Combine like terms: 56.683330883 + -21 = 35.683330883 x = 35.683330883 Simplifying x = 35.683330883Subproblem 2
x + 21 = -56.683330883 Simplifying x + 21 = -56.683330883 Reorder the terms: 21 + x = -56.683330883 Solving 21 + x = -56.683330883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = -56.683330883 + -21 Combine like terms: 21 + -21 = 0 0 + x = -56.683330883 + -21 x = -56.683330883 + -21 Combine like terms: -56.683330883 + -21 = -77.683330883 x = -77.683330883 Simplifying x = -77.683330883Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.683330883, -77.683330883}Solution
x = {35.683330883, -77.683330883}
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