x^2-11x+30.25=0

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Solution for x^2-11x+30.25=0 equation:


Simplifying
x2 + -11x + 30.25 = 0

Reorder the terms:
30.25 + -11x + x2 = 0

Solving
30.25 + -11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-30.25' to each side of the equation.
30.25 + -11x + -30.25 + x2 = 0 + -30.25

Reorder the terms:
30.25 + -30.25 + -11x + x2 = 0 + -30.25

Combine like terms: 30.25 + -30.25 = 0.00
0.00 + -11x + x2 = 0 + -30.25
-11x + x2 = 0 + -30.25

Combine like terms: 0 + -30.25 = -30.25
-11x + x2 = -30.25

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -30.25 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -30.25 + 30.25

Combine like terms: -30.25 + 30.25 = 0.00
30.25 + -11x + x2 = 0.00

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(x + -5.5) equal to 0.00 and 0.00.

Subproblem 1

x + -5.5 = 0.00 Simplifying x + -5.5 = 0.00 Reorder the terms: -5.5 + x = 0.00 Solving -5.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 0.00 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 0.00 + 5.5 x = 0.00 + 5.5 Combine like terms: 0.00 + 5.5 = 5.5 x = 5.5 Simplifying x = 5.5

Subproblem 2

x + -5.5 = 0.00 Simplifying x + -5.5 = 0.00 Reorder the terms: -5.5 + x = 0.00 Solving -5.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 0.00 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 0.00 + 5.5 x = 0.00 + 5.5 Combine like terms: 0.00 + 5.5 = 5.5 x = 5.5 Simplifying x = 5.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.5, 5.5}

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