x^2-5x+1=10

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Solution for x^2-5x+1=10 equation:


Simplifying
x2 + -5x + 1 = 10

Reorder the terms:
1 + -5x + x2 = 10

Solving
1 + -5x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
1 + -10 + -5x + x2 = 10 + -10

Combine like terms: 1 + -10 = -9
-9 + -5x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-9 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -5x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -5x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -5x + x2 = 0 + 9
-5x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-5x + x2 = 9

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 9 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 9 + 6.25

Combine like terms: 9 + 6.25 = 15.25
6.25 + -5x + x2 = 15.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.905124838 and -3.905124838.

Subproblem 1

x + -2.5 = 3.905124838 Simplifying x + -2.5 = 3.905124838 Reorder the terms: -2.5 + x = 3.905124838 Solving -2.5 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.905124838 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.905124838 + 2.5 x = 3.905124838 + 2.5 Combine like terms: 3.905124838 + 2.5 = 6.405124838 x = 6.405124838 Simplifying x = 6.405124838

Subproblem 2

x + -2.5 = -3.905124838 Simplifying x + -2.5 = -3.905124838 Reorder the terms: -2.5 + x = -3.905124838 Solving -2.5 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.905124838 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.905124838 + 2.5 x = -3.905124838 + 2.5 Combine like terms: -3.905124838 + 2.5 = -1.405124838 x = -1.405124838 Simplifying x = -1.405124838

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.405124838, -1.405124838}

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