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Simplifying x2 + -80x + -160 = 0 Reorder the terms: -160 + -80x + x2 = 0 Solving -160 + -80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + -80x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + -80x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -80x + x2 = 0 + 160 -80x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 -80x + x2 = 160 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = 160 + 1600 Reorder the terms: 1600 + -80x + x2 = 160 + 1600 Combine like terms: 160 + 1600 = 1760 1600 + -80x + x2 = 1760 Factor a perfect square on the left side: (x + -40)(x + -40) = 1760 Calculate the square root of the right side: 41.952353927 Break this problem into two subproblems by setting (x + -40) equal to 41.952353927 and -41.952353927.Subproblem 1
x + -40 = 41.952353927 Simplifying x + -40 = 41.952353927 Reorder the terms: -40 + x = 41.952353927 Solving -40 + x = 41.952353927 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 41.952353927 + 40 Combine like terms: -40 + 40 = 0 0 + x = 41.952353927 + 40 x = 41.952353927 + 40 Combine like terms: 41.952353927 + 40 = 81.952353927 x = 81.952353927 Simplifying x = 81.952353927Subproblem 2
x + -40 = -41.952353927 Simplifying x + -40 = -41.952353927 Reorder the terms: -40 + x = -41.952353927 Solving -40 + x = -41.952353927 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -41.952353927 + 40 Combine like terms: -40 + 40 = 0 0 + x = -41.952353927 + 40 x = -41.952353927 + 40 Combine like terms: -41.952353927 + 40 = -1.952353927 x = -1.952353927 Simplifying x = -1.952353927Solution
The solution to the problem is based on the solutions from the subproblems. x = {81.952353927, -1.952353927}
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