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Simplifying x2 + -40x + 40 = 0 Reorder the terms: 40 + -40x + x2 = 0 Solving 40 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -40x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -40x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -40x + x2 = 0 + -40 -40x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -40x + x2 = -40 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 = -40 + 400 Reorder the terms: 400 + -40x + x2 = -40 + 400 Combine like terms: -40 + 400 = 360 400 + -40x + x2 = 360 Factor a perfect square on the left side: (x + -20)(x + -20) = 360 Calculate the square root of the right side: 18.973665961 Break this problem into two subproblems by setting (x + -20) equal to 18.973665961 and -18.973665961.Subproblem 1
x + -20 = 18.973665961 Simplifying x + -20 = 18.973665961 Reorder the terms: -20 + x = 18.973665961 Solving -20 + x = 18.973665961 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 = 18.973665961 + 20 Combine like terms: -20 + 20 = 0 0 + x = 18.973665961 + 20 x = 18.973665961 + 20 Combine like terms: 18.973665961 + 20 = 38.973665961 x = 38.973665961 Simplifying x = 38.973665961Subproblem 2
x + -20 = -18.973665961 Simplifying x + -20 = -18.973665961 Reorder the terms: -20 + x = -18.973665961 Solving -20 + x = -18.973665961 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 = -18.973665961 + 20 Combine like terms: -20 + 20 = 0 0 + x = -18.973665961 + 20 x = -18.973665961 + 20 Combine like terms: -18.973665961 + 20 = 1.026334039 x = 1.026334039 Simplifying x = 1.026334039Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.973665961, 1.026334039}
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