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Simplifying x2 + -38x + 343 = 0 Reorder the terms: 343 + -38x + x2 = 0 Solving 343 + -38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-343' to each side of the equation. 343 + -38x + -343 + x2 = 0 + -343 Reorder the terms: 343 + -343 + -38x + x2 = 0 + -343 Combine like terms: 343 + -343 = 0 0 + -38x + x2 = 0 + -343 -38x + x2 = 0 + -343 Combine like terms: 0 + -343 = -343 -38x + x2 = -343 The x term is -38x. Take half its coefficient (-19). Square it (361) and add it to both sides. Add '361' to each side of the equation. -38x + 361 + x2 = -343 + 361 Reorder the terms: 361 + -38x + x2 = -343 + 361 Combine like terms: -343 + 361 = 18 361 + -38x + x2 = 18 Factor a perfect square on the left side: (x + -19)(x + -19) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + -19) equal to 4.242640687 and -4.242640687.Subproblem 1
x + -19 = 4.242640687 Simplifying x + -19 = 4.242640687 Reorder the terms: -19 + x = 4.242640687 Solving -19 + x = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 4.242640687 + 19 Combine like terms: -19 + 19 = 0 0 + x = 4.242640687 + 19 x = 4.242640687 + 19 Combine like terms: 4.242640687 + 19 = 23.242640687 x = 23.242640687 Simplifying x = 23.242640687Subproblem 2
x + -19 = -4.242640687 Simplifying x + -19 = -4.242640687 Reorder the terms: -19 + x = -4.242640687 Solving -19 + x = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = -4.242640687 + 19 Combine like terms: -19 + 19 = 0 0 + x = -4.242640687 + 19 x = -4.242640687 + 19 Combine like terms: -4.242640687 + 19 = 14.757359313 x = 14.757359313 Simplifying x = 14.757359313Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.242640687, 14.757359313}
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