x^2-2x-247=0

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Solution for x^2-2x-247=0 equation:


Simplifying
x2 + -2x + -247 = 0

Reorder the terms:
-247 + -2x + x2 = 0

Solving
-247 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '247' to each side of the equation.
-247 + -2x + 247 + x2 = 0 + 247

Reorder the terms:
-247 + 247 + -2x + x2 = 0 + 247

Combine like terms: -247 + 247 = 0
0 + -2x + x2 = 0 + 247
-2x + x2 = 0 + 247

Combine like terms: 0 + 247 = 247
-2x + x2 = 247

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 247 + 1

Reorder the terms:
1 + -2x + x2 = 247 + 1

Combine like terms: 247 + 1 = 248
1 + -2x + x2 = 248

Factor a perfect square on the left side:
(x + -1)(x + -1) = 248

Calculate the square root of the right side: 15.748015748

Break this problem into two subproblems by setting 
(x + -1) equal to 15.748015748 and -15.748015748.

Subproblem 1

x + -1 = 15.748015748 Simplifying x + -1 = 15.748015748 Reorder the terms: -1 + x = 15.748015748 Solving -1 + x = 15.748015748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 15.748015748 + 1 Combine like terms: -1 + 1 = 0 0 + x = 15.748015748 + 1 x = 15.748015748 + 1 Combine like terms: 15.748015748 + 1 = 16.748015748 x = 16.748015748 Simplifying x = 16.748015748

Subproblem 2

x + -1 = -15.748015748 Simplifying x + -1 = -15.748015748 Reorder the terms: -1 + x = -15.748015748 Solving -1 + x = -15.748015748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -15.748015748 + 1 Combine like terms: -1 + 1 = 0 0 + x = -15.748015748 + 1 x = -15.748015748 + 1 Combine like terms: -15.748015748 + 1 = -14.748015748 x = -14.748015748 Simplifying x = -14.748015748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.748015748, -14.748015748}

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