x+1=x^2-25-25x

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


Simplifying
x + 1 = x2 + -25 + -25x

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

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

Solving
1 + x = -25 + -25x + x2

Solving for variable 'x'.

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

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

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

Reorder the terms:
26 + 26x + -1x2 = -25 + 25 + -25x + 25x + x2 + -1x2

Combine like terms: -25 + 25 = 0
26 + 26x + -1x2 = 0 + -25x + 25x + x2 + -1x2
26 + 26x + -1x2 = -25x + 25x + x2 + -1x2

Combine like terms: -25x + 25x = 0
26 + 26x + -1x2 = 0 + x2 + -1x2
26 + 26x + -1x2 = x2 + -1x2

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

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

Divide each side by '-1'.
-26 + -26x + x2 = 0

Move the constant term to the right:

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

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

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

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

The x term is -26x.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26x + 169 + x2 = 26 + 169

Reorder the terms:
169 + -26x + x2 = 26 + 169

Combine like terms: 26 + 169 = 195
169 + -26x + x2 = 195

Factor a perfect square on the left side:
(x + -13)(x + -13) = 195

Calculate the square root of the right side: 13.964240044

Break this problem into two subproblems by setting 
(x + -13) equal to 13.964240044 and -13.964240044.

Subproblem 1

x + -13 = 13.964240044 Simplifying x + -13 = 13.964240044 Reorder the terms: -13 + x = 13.964240044 Solving -13 + x = 13.964240044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 13.964240044 + 13 Combine like terms: -13 + 13 = 0 0 + x = 13.964240044 + 13 x = 13.964240044 + 13 Combine like terms: 13.964240044 + 13 = 26.964240044 x = 26.964240044 Simplifying x = 26.964240044

Subproblem 2

x + -13 = -13.964240044 Simplifying x + -13 = -13.964240044 Reorder the terms: -13 + x = -13.964240044 Solving -13 + x = -13.964240044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -13.964240044 + 13 Combine like terms: -13 + 13 = 0 0 + x = -13.964240044 + 13 x = -13.964240044 + 13 Combine like terms: -13.964240044 + 13 = -0.964240044 x = -0.964240044 Simplifying x = -0.964240044

Solution

The solution to the problem is based on the solutions from the subproblems. x = {26.964240044, -0.964240044}

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