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Simplifying x2 + -194x + -1238 = 0 Reorder the terms: -1238 + -194x + x2 = 0 Solving -1238 + -194x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1238' to each side of the equation. -1238 + -194x + 1238 + x2 = 0 + 1238 Reorder the terms: -1238 + 1238 + -194x + x2 = 0 + 1238 Combine like terms: -1238 + 1238 = 0 0 + -194x + x2 = 0 + 1238 -194x + x2 = 0 + 1238 Combine like terms: 0 + 1238 = 1238 -194x + x2 = 1238 The x term is -194x. Take half its coefficient (-97). Square it (9409) and add it to both sides. Add '9409' to each side of the equation. -194x + 9409 + x2 = 1238 + 9409 Reorder the terms: 9409 + -194x + x2 = 1238 + 9409 Combine like terms: 1238 + 9409 = 10647 9409 + -194x + x2 = 10647 Factor a perfect square on the left side: (x + -97)(x + -97) = 10647 Calculate the square root of the right side: 103.184301132 Break this problem into two subproblems by setting (x + -97) equal to 103.184301132 and -103.184301132.Subproblem 1
x + -97 = 103.184301132 Simplifying x + -97 = 103.184301132 Reorder the terms: -97 + x = 103.184301132 Solving -97 + x = 103.184301132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '97' to each side of the equation. -97 + 97 + x = 103.184301132 + 97 Combine like terms: -97 + 97 = 0 0 + x = 103.184301132 + 97 x = 103.184301132 + 97 Combine like terms: 103.184301132 + 97 = 200.184301132 x = 200.184301132 Simplifying x = 200.184301132Subproblem 2
x + -97 = -103.184301132 Simplifying x + -97 = -103.184301132 Reorder the terms: -97 + x = -103.184301132 Solving -97 + x = -103.184301132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '97' to each side of the equation. -97 + 97 + x = -103.184301132 + 97 Combine like terms: -97 + 97 = 0 0 + x = -103.184301132 + 97 x = -103.184301132 + 97 Combine like terms: -103.184301132 + 97 = -6.184301132 x = -6.184301132 Simplifying x = -6.184301132Solution
The solution to the problem is based on the solutions from the subproblems. x = {200.184301132, -6.184301132}
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