x^2-10x-25=1

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Solution for x^2-10x-25=1 equation:


Simplifying
x2 + -10x + -25 = 1

Reorder the terms:
-25 + -10x + x2 = 1

Solving
-25 + -10x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
-25 + -1 + -10x + x2 = 1 + -1

Combine like terms: -25 + -1 = -26
-26 + -10x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-26 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + -10x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + -10x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -10x + x2 = 0 + 26
-10x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
-10x + x2 = 26

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 26 + 25

Reorder the terms:
25 + -10x + x2 = 26 + 25

Combine like terms: 26 + 25 = 51
25 + -10x + x2 = 51

Factor a perfect square on the left side:
(x + -5)(x + -5) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(x + -5) equal to 7.141428429 and -7.141428429.

Subproblem 1

x + -5 = 7.141428429 Simplifying x + -5 = 7.141428429 Reorder the terms: -5 + x = 7.141428429 Solving -5 + x = 7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 7.141428429 + 5 Combine like terms: -5 + 5 = 0 0 + x = 7.141428429 + 5 x = 7.141428429 + 5 Combine like terms: 7.141428429 + 5 = 12.141428429 x = 12.141428429 Simplifying x = 12.141428429

Subproblem 2

x + -5 = -7.141428429 Simplifying x + -5 = -7.141428429 Reorder the terms: -5 + x = -7.141428429 Solving -5 + x = -7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -7.141428429 + 5 Combine like terms: -5 + 5 = 0 0 + x = -7.141428429 + 5 x = -7.141428429 + 5 Combine like terms: -7.141428429 + 5 = -2.141428429 x = -2.141428429 Simplifying x = -2.141428429

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.141428429, -2.141428429}

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