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Simplifying x2 + -55x + -722 = 0 Reorder the terms: -722 + -55x + x2 = 0 Solving -722 + -55x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '722' to each side of the equation. -722 + -55x + 722 + x2 = 0 + 722 Reorder the terms: -722 + 722 + -55x + x2 = 0 + 722 Combine like terms: -722 + 722 = 0 0 + -55x + x2 = 0 + 722 -55x + x2 = 0 + 722 Combine like terms: 0 + 722 = 722 -55x + x2 = 722 The x term is -55x. Take half its coefficient (-27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. -55x + 756.25 + x2 = 722 + 756.25 Reorder the terms: 756.25 + -55x + x2 = 722 + 756.25 Combine like terms: 722 + 756.25 = 1478.25 756.25 + -55x + x2 = 1478.25 Factor a perfect square on the left side: (x + -27.5)(x + -27.5) = 1478.25 Calculate the square root of the right side: 38.448016854 Break this problem into two subproblems by setting (x + -27.5) equal to 38.448016854 and -38.448016854.Subproblem 1
x + -27.5 = 38.448016854 Simplifying x + -27.5 = 38.448016854 Reorder the terms: -27.5 + x = 38.448016854 Solving -27.5 + x = 38.448016854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = 38.448016854 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = 38.448016854 + 27.5 x = 38.448016854 + 27.5 Combine like terms: 38.448016854 + 27.5 = 65.948016854 x = 65.948016854 Simplifying x = 65.948016854Subproblem 2
x + -27.5 = -38.448016854 Simplifying x + -27.5 = -38.448016854 Reorder the terms: -27.5 + x = -38.448016854 Solving -27.5 + x = -38.448016854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = -38.448016854 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = -38.448016854 + 27.5 x = -38.448016854 + 27.5 Combine like terms: -38.448016854 + 27.5 = -10.948016854 x = -10.948016854 Simplifying x = -10.948016854Solution
The solution to the problem is based on the solutions from the subproblems. x = {65.948016854, -10.948016854}
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