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Simplifying x2 + 56x + -24 = 0 Reorder the terms: -24 + 56x + x2 = 0 Solving -24 + 56x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 56x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 56x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 56x + x2 = 0 + 24 56x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 56x + x2 = 24 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 = 24 + 784 Reorder the terms: 784 + 56x + x2 = 24 + 784 Combine like terms: 24 + 784 = 808 784 + 56x + x2 = 808 Factor a perfect square on the left side: (x + 28)(x + 28) = 808 Calculate the square root of the right side: 28.425340807 Break this problem into two subproblems by setting (x + 28) equal to 28.425340807 and -28.425340807.Subproblem 1
x + 28 = 28.425340807 Simplifying x + 28 = 28.425340807 Reorder the terms: 28 + x = 28.425340807 Solving 28 + x = 28.425340807 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 = 28.425340807 + -28 Combine like terms: 28 + -28 = 0 0 + x = 28.425340807 + -28 x = 28.425340807 + -28 Combine like terms: 28.425340807 + -28 = 0.425340807 x = 0.425340807 Simplifying x = 0.425340807Subproblem 2
x + 28 = -28.425340807 Simplifying x + 28 = -28.425340807 Reorder the terms: 28 + x = -28.425340807 Solving 28 + x = -28.425340807 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 = -28.425340807 + -28 Combine like terms: 28 + -28 = 0 0 + x = -28.425340807 + -28 x = -28.425340807 + -28 Combine like terms: -28.425340807 + -28 = -56.425340807 x = -56.425340807 Simplifying x = -56.425340807Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.425340807, -56.425340807}
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