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Simplifying x2 + 56x + -510 = 0 Reorder the terms: -510 + 56x + x2 = 0 Solving -510 + 56x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '510' to each side of the equation. -510 + 56x + 510 + x2 = 0 + 510 Reorder the terms: -510 + 510 + 56x + x2 = 0 + 510 Combine like terms: -510 + 510 = 0 0 + 56x + x2 = 0 + 510 56x + x2 = 0 + 510 Combine like terms: 0 + 510 = 510 56x + x2 = 510 The x term is 56x. Take half its coefficient (28). Square it (784) and add it to both sides. Add '784' to each side of the equation. 56x + 784 + x2 = 510 + 784 Reorder the terms: 784 + 56x + x2 = 510 + 784 Combine like terms: 510 + 784 = 1294 784 + 56x + x2 = 1294 Factor a perfect square on the left side: (x + 28)(x + 28) = 1294 Calculate the square root of the right side: 35.972211497 Break this problem into two subproblems by setting (x + 28) equal to 35.972211497 and -35.972211497.Subproblem 1
x + 28 = 35.972211497 Simplifying x + 28 = 35.972211497 Reorder the terms: 28 + x = 35.972211497 Solving 28 + x = 35.972211497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + x = 35.972211497 + -28 Combine like terms: 28 + -28 = 0 0 + x = 35.972211497 + -28 x = 35.972211497 + -28 Combine like terms: 35.972211497 + -28 = 7.972211497 x = 7.972211497 Simplifying x = 7.972211497Subproblem 2
x + 28 = -35.972211497 Simplifying x + 28 = -35.972211497 Reorder the terms: 28 + x = -35.972211497 Solving 28 + x = -35.972211497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + x = -35.972211497 + -28 Combine like terms: 28 + -28 = 0 0 + x = -35.972211497 + -28 x = -35.972211497 + -28 Combine like terms: -35.972211497 + -28 = -63.972211497 x = -63.972211497 Simplifying x = -63.972211497Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.972211497, -63.972211497}
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