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Simplifying x2 + -80x + 400 = 0 Reorder the terms: 400 + -80x + x2 = 0 Solving 400 + -80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-400' to each side of the equation. 400 + -80x + -400 + x2 = 0 + -400 Reorder the terms: 400 + -400 + -80x + x2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -80x + x2 = 0 + -400 -80x + x2 = 0 + -400 Combine like terms: 0 + -400 = -400 -80x + x2 = -400 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 = -400 + 1600 Reorder the terms: 1600 + -80x + x2 = -400 + 1600 Combine like terms: -400 + 1600 = 1200 1600 + -80x + x2 = 1200 Factor a perfect square on the left side: (x + -40)(x + -40) = 1200 Calculate the square root of the right side: 34.641016151 Break this problem into two subproblems by setting (x + -40) equal to 34.641016151 and -34.641016151.Subproblem 1
x + -40 = 34.641016151 Simplifying x + -40 = 34.641016151 Reorder the terms: -40 + x = 34.641016151 Solving -40 + x = 34.641016151 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 = 34.641016151 + 40 Combine like terms: -40 + 40 = 0 0 + x = 34.641016151 + 40 x = 34.641016151 + 40 Combine like terms: 34.641016151 + 40 = 74.641016151 x = 74.641016151 Simplifying x = 74.641016151Subproblem 2
x + -40 = -34.641016151 Simplifying x + -40 = -34.641016151 Reorder the terms: -40 + x = -34.641016151 Solving -40 + x = -34.641016151 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 = -34.641016151 + 40 Combine like terms: -40 + 40 = 0 0 + x = -34.641016151 + 40 x = -34.641016151 + 40 Combine like terms: -34.641016151 + 40 = 5.358983849 x = 5.358983849 Simplifying x = 5.358983849Solution
The solution to the problem is based on the solutions from the subproblems. x = {74.641016151, 5.358983849}
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