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Simplifying x2 + -40x + 320 = 0 Reorder the terms: 320 + -40x + x2 = 0 Solving 320 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-320' to each side of the equation. 320 + -40x + -320 + x2 = 0 + -320 Reorder the terms: 320 + -320 + -40x + x2 = 0 + -320 Combine like terms: 320 + -320 = 0 0 + -40x + x2 = 0 + -320 -40x + x2 = 0 + -320 Combine like terms: 0 + -320 = -320 -40x + x2 = -320 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -320 + 400 Reorder the terms: 400 + -40x + x2 = -320 + 400 Combine like terms: -320 + 400 = 80 400 + -40x + x2 = 80 Factor a perfect square on the left side: (x + -20)(x + -20) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + -20) equal to 8.94427191 and -8.94427191.Subproblem 1
x + -20 = 8.94427191 Simplifying x + -20 = 8.94427191 Reorder the terms: -20 + x = 8.94427191 Solving -20 + x = 8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 8.94427191 + 20 Combine like terms: -20 + 20 = 0 0 + x = 8.94427191 + 20 x = 8.94427191 + 20 Combine like terms: 8.94427191 + 20 = 28.94427191 x = 28.94427191 Simplifying x = 28.94427191Subproblem 2
x + -20 = -8.94427191 Simplifying x + -20 = -8.94427191 Reorder the terms: -20 + x = -8.94427191 Solving -20 + x = -8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -8.94427191 + 20 Combine like terms: -20 + 20 = 0 0 + x = -8.94427191 + 20 x = -8.94427191 + 20 Combine like terms: -8.94427191 + 20 = 11.05572809 x = 11.05572809 Simplifying x = 11.05572809Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.94427191, 11.05572809}
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