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Simplifying x2 + -38x + 224 = 0 Reorder the terms: 224 + -38x + x2 = 0 Solving 224 + -38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-224' to each side of the equation. 224 + -38x + -224 + x2 = 0 + -224 Reorder the terms: 224 + -224 + -38x + x2 = 0 + -224 Combine like terms: 224 + -224 = 0 0 + -38x + x2 = 0 + -224 -38x + x2 = 0 + -224 Combine like terms: 0 + -224 = -224 -38x + x2 = -224 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 = -224 + 361 Reorder the terms: 361 + -38x + x2 = -224 + 361 Combine like terms: -224 + 361 = 137 361 + -38x + x2 = 137 Factor a perfect square on the left side: (x + -19)(x + -19) = 137 Calculate the square root of the right side: 11.704699911 Break this problem into two subproblems by setting (x + -19) equal to 11.704699911 and -11.704699911.Subproblem 1
x + -19 = 11.704699911 Simplifying x + -19 = 11.704699911 Reorder the terms: -19 + x = 11.704699911 Solving -19 + x = 11.704699911 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 = 11.704699911 + 19 Combine like terms: -19 + 19 = 0 0 + x = 11.704699911 + 19 x = 11.704699911 + 19 Combine like terms: 11.704699911 + 19 = 30.704699911 x = 30.704699911 Simplifying x = 30.704699911Subproblem 2
x + -19 = -11.704699911 Simplifying x + -19 = -11.704699911 Reorder the terms: -19 + x = -11.704699911 Solving -19 + x = -11.704699911 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 = -11.704699911 + 19 Combine like terms: -19 + 19 = 0 0 + x = -11.704699911 + 19 x = -11.704699911 + 19 Combine like terms: -11.704699911 + 19 = 7.295300089 x = 7.295300089 Simplifying x = 7.295300089Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.704699911, 7.295300089}
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