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Simplifying x2 + -328x + 1280 = 0 Reorder the terms: 1280 + -328x + x2 = 0 Solving 1280 + -328x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1280' to each side of the equation. 1280 + -328x + -1280 + x2 = 0 + -1280 Reorder the terms: 1280 + -1280 + -328x + x2 = 0 + -1280 Combine like terms: 1280 + -1280 = 0 0 + -328x + x2 = 0 + -1280 -328x + x2 = 0 + -1280 Combine like terms: 0 + -1280 = -1280 -328x + x2 = -1280 The x term is -328x. Take half its coefficient (-164). Square it (26896) and add it to both sides. Add '26896' to each side of the equation. -328x + 26896 + x2 = -1280 + 26896 Reorder the terms: 26896 + -328x + x2 = -1280 + 26896 Combine like terms: -1280 + 26896 = 25616 26896 + -328x + x2 = 25616 Factor a perfect square on the left side: (x + -164)(x + -164) = 25616 Calculate the square root of the right side: 160.04999219 Break this problem into two subproblems by setting (x + -164) equal to 160.04999219 and -160.04999219.Subproblem 1
x + -164 = 160.04999219 Simplifying x + -164 = 160.04999219 Reorder the terms: -164 + x = 160.04999219 Solving -164 + x = 160.04999219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '164' to each side of the equation. -164 + 164 + x = 160.04999219 + 164 Combine like terms: -164 + 164 = 0 0 + x = 160.04999219 + 164 x = 160.04999219 + 164 Combine like terms: 160.04999219 + 164 = 324.04999219 x = 324.04999219 Simplifying x = 324.04999219Subproblem 2
x + -164 = -160.04999219 Simplifying x + -164 = -160.04999219 Reorder the terms: -164 + x = -160.04999219 Solving -164 + x = -160.04999219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '164' to each side of the equation. -164 + 164 + x = -160.04999219 + 164 Combine like terms: -164 + 164 = 0 0 + x = -160.04999219 + 164 x = -160.04999219 + 164 Combine like terms: -160.04999219 + 164 = 3.95000781 x = 3.95000781 Simplifying x = 3.95000781Solution
The solution to the problem is based on the solutions from the subproblems. x = {324.04999219, 3.95000781}
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