0=x^2-2x-7

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Solution for 0=x^2-2x-7 equation:


Simplifying
0 = x2 + -2x + -7

Reorder the terms:
0 = -7 + -2x + x2

Solving
0 = -7 + -2x + x2

Solving for variable 'x'.

Combine like terms: 0 + 7 = 7
7 + 2x + -1x2 = -7 + -2x + x2 + 7 + 2x + -1x2

Reorder the terms:
7 + 2x + -1x2 = -7 + 7 + -2x + 2x + x2 + -1x2

Combine like terms: -7 + 7 = 0
7 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2
7 + 2x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
7 + 2x + -1x2 = 0 + x2 + -1x2
7 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-7 + -2x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -2x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -2x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x + x2 = 0 + 7
-2x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-2x + x2 = 7

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 = 7 + 1

Reorder the terms:
1 + -2x + x2 = 7 + 1

Combine like terms: 7 + 1 = 8
1 + -2x + x2 = 8

Factor a perfect square on the left side:
(x + -1)(x + -1) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -1) equal to 2.828427125 and -2.828427125.

Subproblem 1

x + -1 = 2.828427125 Simplifying x + -1 = 2.828427125 Reorder the terms: -1 + x = 2.828427125 Solving -1 + x = 2.828427125 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 = 2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.828427125 + 1 x = 2.828427125 + 1 Combine like terms: 2.828427125 + 1 = 3.828427125 x = 3.828427125 Simplifying x = 3.828427125

Subproblem 2

x + -1 = -2.828427125 Simplifying x + -1 = -2.828427125 Reorder the terms: -1 + x = -2.828427125 Solving -1 + x = -2.828427125 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 = -2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.828427125 + 1 x = -2.828427125 + 1 Combine like terms: -2.828427125 + 1 = -1.828427125 x = -1.828427125 Simplifying x = -1.828427125

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.828427125, -1.828427125}

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