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Simplifying x2 + -56x + -384 = 0 Reorder the terms: -384 + -56x + x2 = 0 Solving -384 + -56x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '384' to each side of the equation. -384 + -56x + 384 + x2 = 0 + 384 Reorder the terms: -384 + 384 + -56x + x2 = 0 + 384 Combine like terms: -384 + 384 = 0 0 + -56x + x2 = 0 + 384 -56x + x2 = 0 + 384 Combine like terms: 0 + 384 = 384 -56x + x2 = 384 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 = 384 + 784 Reorder the terms: 784 + -56x + x2 = 384 + 784 Combine like terms: 384 + 784 = 1168 784 + -56x + x2 = 1168 Factor a perfect square on the left side: (x + -28)(x + -28) = 1168 Calculate the square root of the right side: 34.176014981 Break this problem into two subproblems by setting (x + -28) equal to 34.176014981 and -34.176014981.Subproblem 1
x + -28 = 34.176014981 Simplifying x + -28 = 34.176014981 Reorder the terms: -28 + x = 34.176014981 Solving -28 + x = 34.176014981 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 = 34.176014981 + 28 Combine like terms: -28 + 28 = 0 0 + x = 34.176014981 + 28 x = 34.176014981 + 28 Combine like terms: 34.176014981 + 28 = 62.176014981 x = 62.176014981 Simplifying x = 62.176014981Subproblem 2
x + -28 = -34.176014981 Simplifying x + -28 = -34.176014981 Reorder the terms: -28 + x = -34.176014981 Solving -28 + x = -34.176014981 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 = -34.176014981 + 28 Combine like terms: -28 + 28 = 0 0 + x = -34.176014981 + 28 x = -34.176014981 + 28 Combine like terms: -34.176014981 + 28 = -6.176014981 x = -6.176014981 Simplifying x = -6.176014981Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.176014981, -6.176014981}
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