0=x^2-7x+11

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Solution for 0=x^2-7x+11 equation:


Simplifying
0 = x2 + -7x + 11

Reorder the terms:
0 = 11 + -7x + x2

Solving
0 = 11 + -7x + x2

Solving for variable 'x'.

Combine like terms: 0 + -11 = -11
-11 + 7x + -1x2 = 11 + -7x + x2 + -11 + 7x + -1x2

Reorder the terms:
-11 + 7x + -1x2 = 11 + -11 + -7x + 7x + x2 + -1x2

Combine like terms: 11 + -11 = 0
-11 + 7x + -1x2 = 0 + -7x + 7x + x2 + -1x2
-11 + 7x + -1x2 = -7x + 7x + x2 + -1x2

Combine like terms: -7x + 7x = 0
-11 + 7x + -1x2 = 0 + x2 + -1x2
-11 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-11 + 7x + -1x2 = 0

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

Divide each side by '-1'.
11 + -7x + x2 = 0

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -7x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + -7x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -7x + x2 = 0 + -11
-7x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-7x + x2 = -11

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -11 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -11 + 12.25

Combine like terms: -11 + 12.25 = 1.25
12.25 + -7x + x2 = 1.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + -3.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + -3.5 = 1.118033989 Simplifying x + -3.5 = 1.118033989 Reorder the terms: -3.5 + x = 1.118033989 Solving -3.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 1.118033989 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.118033989 + 3.5 x = 1.118033989 + 3.5 Combine like terms: 1.118033989 + 3.5 = 4.618033989 x = 4.618033989 Simplifying x = 4.618033989

Subproblem 2

x + -3.5 = -1.118033989 Simplifying x + -3.5 = -1.118033989 Reorder the terms: -3.5 + x = -1.118033989 Solving -3.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -1.118033989 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.118033989 + 3.5 x = -1.118033989 + 3.5 Combine like terms: -1.118033989 + 3.5 = 2.381966011 x = 2.381966011 Simplifying x = 2.381966011

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.618033989, 2.381966011}

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