q^2-25=10q

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Solution for q^2-25=10q equation:


Simplifying
q2 + -25 = 10q

Reorder the terms:
-25 + q2 = 10q

Solving
-25 + q2 = 10q

Solving for variable 'q'.

Reorder the terms:
-25 + -10q + q2 = 10q + -10q

Combine like terms: 10q + -10q = 0
-25 + -10q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -10q + 25 + q2 = 0 + 25

Reorder the terms:
-25 + 25 + -10q + q2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -10q + q2 = 0 + 25
-10q + q2 = 0 + 25

Combine like terms: 0 + 25 = 25
-10q + q2 = 25

The q term is -10q.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10q + 25 + q2 = 25 + 25

Reorder the terms:
25 + -10q + q2 = 25 + 25

Combine like terms: 25 + 25 = 50
25 + -10q + q2 = 50

Factor a perfect square on the left side:
(q + -5)(q + -5) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(q + -5) equal to 7.071067812 and -7.071067812.

Subproblem 1

q + -5 = 7.071067812 Simplifying q + -5 = 7.071067812 Reorder the terms: -5 + q = 7.071067812 Solving -5 + q = 7.071067812 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + q = 7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + q = 7.071067812 + 5 q = 7.071067812 + 5 Combine like terms: 7.071067812 + 5 = 12.071067812 q = 12.071067812 Simplifying q = 12.071067812

Subproblem 2

q + -5 = -7.071067812 Simplifying q + -5 = -7.071067812 Reorder the terms: -5 + q = -7.071067812 Solving -5 + q = -7.071067812 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + q = -7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + q = -7.071067812 + 5 q = -7.071067812 + 5 Combine like terms: -7.071067812 + 5 = -2.071067812 q = -2.071067812 Simplifying q = -2.071067812

Solution

The solution to the problem is based on the solutions from the subproblems. q = {12.071067812, -2.071067812}

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