x^2-2x+13=12.25

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Solution for x^2-2x+13=12.25 equation:


Simplifying
x2 + -2x + 13 = 12.25

Reorder the terms:
13 + -2x + x2 = 12.25

Solving
13 + -2x + x2 = 12.25

Solving for variable 'x'.

Reorder the terms:
13 + -12.25 + -2x + x2 = 12.25 + -12.25

Combine like terms: 13 + -12.25 = 0.75
0.75 + -2x + x2 = 12.25 + -12.25

Combine like terms: 12.25 + -12.25 = 0.00
0.75 + -2x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -2x + -0.75 + x2 = 0.00 + -0.75

Reorder the terms:
0.75 + -0.75 + -2x + x2 = 0.00 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -2x + x2 = 0.00 + -0.75
-2x + x2 = 0.00 + -0.75

Combine like terms: 0.00 + -0.75 = -0.75
-2x + x2 = -0.75

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 = -0.75 + 1

Reorder the terms:
1 + -2x + x2 = -0.75 + 1

Combine like terms: -0.75 + 1 = 0.25
1 + -2x + x2 = 0.25

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.25

Calculate the square root of the right side: 0.5

Break this problem into two subproblems by setting 
(x + -1) equal to 0.5 and -0.5.

Subproblem 1

x + -1 = 0.5 Simplifying x + -1 = 0.5 Reorder the terms: -1 + x = 0.5 Solving -1 + x = 0.5 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 = 0.5 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.5 + 1 x = 0.5 + 1 Combine like terms: 0.5 + 1 = 1.5 x = 1.5 Simplifying x = 1.5

Subproblem 2

x + -1 = -0.5 Simplifying x + -1 = -0.5 Reorder the terms: -1 + x = -0.5 Solving -1 + x = -0.5 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 = -0.5 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.5 + 1 x = -0.5 + 1 Combine like terms: -0.5 + 1 = 0.5 x = 0.5 Simplifying x = 0.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.5, 0.5}

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