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Simplifying x2 + -40x + 125 = 0 Reorder the terms: 125 + -40x + x2 = 0 Solving 125 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-125' to each side of the equation. 125 + -40x + -125 + x2 = 0 + -125 Reorder the terms: 125 + -125 + -40x + x2 = 0 + -125 Combine like terms: 125 + -125 = 0 0 + -40x + x2 = 0 + -125 -40x + x2 = 0 + -125 Combine like terms: 0 + -125 = -125 -40x + x2 = -125 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 = -125 + 400 Reorder the terms: 400 + -40x + x2 = -125 + 400 Combine like terms: -125 + 400 = 275 400 + -40x + x2 = 275 Factor a perfect square on the left side: (x + -20)(x + -20) = 275 Calculate the square root of the right side: 16.583123952 Break this problem into two subproblems by setting (x + -20) equal to 16.583123952 and -16.583123952.Subproblem 1
x + -20 = 16.583123952 Simplifying x + -20 = 16.583123952 Reorder the terms: -20 + x = 16.583123952 Solving -20 + x = 16.583123952 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 = 16.583123952 + 20 Combine like terms: -20 + 20 = 0 0 + x = 16.583123952 + 20 x = 16.583123952 + 20 Combine like terms: 16.583123952 + 20 = 36.583123952 x = 36.583123952 Simplifying x = 36.583123952Subproblem 2
x + -20 = -16.583123952 Simplifying x + -20 = -16.583123952 Reorder the terms: -20 + x = -16.583123952 Solving -20 + x = -16.583123952 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 = -16.583123952 + 20 Combine like terms: -20 + 20 = 0 0 + x = -16.583123952 + 20 x = -16.583123952 + 20 Combine like terms: -16.583123952 + 20 = 3.416876048 x = 3.416876048 Simplifying x = 3.416876048Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.583123952, 3.416876048}
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