0=x^2-14x+25

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Solution for 0=x^2-14x+25 equation:


Simplifying
0 = x2 + -14x + 25

Reorder the terms:
0 = 25 + -14x + x2

Solving
0 = 25 + -14x + x2

Solving for variable 'x'.

Combine like terms: 0 + -25 = -25
-25 + 14x + -1x2 = 25 + -14x + x2 + -25 + 14x + -1x2

Reorder the terms:
-25 + 14x + -1x2 = 25 + -25 + -14x + 14x + x2 + -1x2

Combine like terms: 25 + -25 = 0
-25 + 14x + -1x2 = 0 + -14x + 14x + x2 + -1x2
-25 + 14x + -1x2 = -14x + 14x + x2 + -1x2

Combine like terms: -14x + 14x = 0
-25 + 14x + -1x2 = 0 + x2 + -1x2
-25 + 14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-25 + 14x + -1x2 = 0

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

Divide each side by '-1'.
25 + -14x + x2 = 0

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -14x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + -14x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -14x + x2 = 0 + -25
-14x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
-14x + x2 = -25

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -25 + 49

Reorder the terms:
49 + -14x + x2 = -25 + 49

Combine like terms: -25 + 49 = 24
49 + -14x + x2 = 24

Factor a perfect square on the left side:
(x + -7)(x + -7) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + -7) equal to 4.898979486 and -4.898979486.

Subproblem 1

x + -7 = 4.898979486 Simplifying x + -7 = 4.898979486 Reorder the terms: -7 + x = 4.898979486 Solving -7 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 4.898979486 + 7 Combine like terms: -7 + 7 = 0 0 + x = 4.898979486 + 7 x = 4.898979486 + 7 Combine like terms: 4.898979486 + 7 = 11.898979486 x = 11.898979486 Simplifying x = 11.898979486

Subproblem 2

x + -7 = -4.898979486 Simplifying x + -7 = -4.898979486 Reorder the terms: -7 + x = -4.898979486 Solving -7 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -4.898979486 + 7 Combine like terms: -7 + 7 = 0 0 + x = -4.898979486 + 7 x = -4.898979486 + 7 Combine like terms: -4.898979486 + 7 = 2.101020514 x = 2.101020514 Simplifying x = 2.101020514

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.898979486, 2.101020514}

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