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Simplifying x2 + -56x + -768 = 0 Reorder the terms: -768 + -56x + x2 = 0 Solving -768 + -56x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '768' to each side of the equation. -768 + -56x + 768 + x2 = 0 + 768 Reorder the terms: -768 + 768 + -56x + x2 = 0 + 768 Combine like terms: -768 + 768 = 0 0 + -56x + x2 = 0 + 768 -56x + x2 = 0 + 768 Combine like terms: 0 + 768 = 768 -56x + x2 = 768 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 = 768 + 784 Reorder the terms: 784 + -56x + x2 = 768 + 784 Combine like terms: 768 + 784 = 1552 784 + -56x + x2 = 1552 Factor a perfect square on the left side: (x + -28)(x + -28) = 1552 Calculate the square root of the right side: 39.395431207 Break this problem into two subproblems by setting (x + -28) equal to 39.395431207 and -39.395431207.Subproblem 1
x + -28 = 39.395431207 Simplifying x + -28 = 39.395431207 Reorder the terms: -28 + x = 39.395431207 Solving -28 + x = 39.395431207 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 = 39.395431207 + 28 Combine like terms: -28 + 28 = 0 0 + x = 39.395431207 + 28 x = 39.395431207 + 28 Combine like terms: 39.395431207 + 28 = 67.395431207 x = 67.395431207 Simplifying x = 67.395431207Subproblem 2
x + -28 = -39.395431207 Simplifying x + -28 = -39.395431207 Reorder the terms: -28 + x = -39.395431207 Solving -28 + x = -39.395431207 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 = -39.395431207 + 28 Combine like terms: -28 + 28 = 0 0 + x = -39.395431207 + 28 x = -39.395431207 + 28 Combine like terms: -39.395431207 + 28 = -11.395431207 x = -11.395431207 Simplifying x = -11.395431207Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.395431207, -11.395431207}
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