q^2-14q+25=0

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


Simplifying
q2 + -14q + 25 = 0

Reorder the terms:
25 + -14q + q2 = 0

Solving
25 + -14q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -14q + -25 + q2 = 0 + -25

Reorder the terms:
25 + -25 + -14q + q2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -14q + q2 = 0 + -25
-14q + q2 = 0 + -25

Combine like terms: 0 + -25 = -25
-14q + q2 = -25

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

Add '49' to each side of the equation.
-14q + 49 + q2 = -25 + 49

Reorder the terms:
49 + -14q + q2 = -25 + 49

Combine like terms: -25 + 49 = 24
49 + -14q + q2 = 24

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

Calculate the square root of the right side: 4.898979486

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

Subproblem 1

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

Subproblem 2

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

Solution

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

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