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Simplifying x2 + -40x + 13 = 0 Reorder the terms: 13 + -40x + x2 = 0 Solving 13 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -40x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -40x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -40x + x2 = 0 + -13 -40x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -40x + x2 = -13 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 = -13 + 400 Reorder the terms: 400 + -40x + x2 = -13 + 400 Combine like terms: -13 + 400 = 387 400 + -40x + x2 = 387 Factor a perfect square on the left side: (x + -20)(x + -20) = 387 Calculate the square root of the right side: 19.672315573 Break this problem into two subproblems by setting (x + -20) equal to 19.672315573 and -19.672315573.Subproblem 1
x + -20 = 19.672315573 Simplifying x + -20 = 19.672315573 Reorder the terms: -20 + x = 19.672315573 Solving -20 + x = 19.672315573 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 = 19.672315573 + 20 Combine like terms: -20 + 20 = 0 0 + x = 19.672315573 + 20 x = 19.672315573 + 20 Combine like terms: 19.672315573 + 20 = 39.672315573 x = 39.672315573 Simplifying x = 39.672315573Subproblem 2
x + -20 = -19.672315573 Simplifying x + -20 = -19.672315573 Reorder the terms: -20 + x = -19.672315573 Solving -20 + x = -19.672315573 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 = -19.672315573 + 20 Combine like terms: -20 + 20 = 0 0 + x = -19.672315573 + 20 x = -19.672315573 + 20 Combine like terms: -19.672315573 + 20 = 0.327684427 x = 0.327684427 Simplifying x = 0.327684427Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.672315573, 0.327684427}
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