q^2+75q-6250=q

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Solution for q^2+75q-6250=q equation:


Simplifying
q2 + 75q + -6250 = q

Reorder the terms:
-6250 + 75q + q2 = q

Solving
-6250 + 75q + q2 = q

Solving for variable 'q'.

Reorder the terms:
-6250 + 75q + -1q + q2 = q + -1q

Combine like terms: 75q + -1q = 74q
-6250 + 74q + q2 = q + -1q

Combine like terms: q + -1q = 0
-6250 + 74q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6250' to each side of the equation.
-6250 + 74q + 6250 + q2 = 0 + 6250

Reorder the terms:
-6250 + 6250 + 74q + q2 = 0 + 6250

Combine like terms: -6250 + 6250 = 0
0 + 74q + q2 = 0 + 6250
74q + q2 = 0 + 6250

Combine like terms: 0 + 6250 = 6250
74q + q2 = 6250

The q term is 74q.  Take half its coefficient (37).
Square it (1369) and add it to both sides.

Add '1369' to each side of the equation.
74q + 1369 + q2 = 6250 + 1369

Reorder the terms:
1369 + 74q + q2 = 6250 + 1369

Combine like terms: 6250 + 1369 = 7619
1369 + 74q + q2 = 7619

Factor a perfect square on the left side:
(q + 37)(q + 37) = 7619

Calculate the square root of the right side: 87.286883322

Break this problem into two subproblems by setting 
(q + 37) equal to 87.286883322 and -87.286883322.

Subproblem 1

q + 37 = 87.286883322 Simplifying q + 37 = 87.286883322 Reorder the terms: 37 + q = 87.286883322 Solving 37 + q = 87.286883322 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + q = 87.286883322 + -37 Combine like terms: 37 + -37 = 0 0 + q = 87.286883322 + -37 q = 87.286883322 + -37 Combine like terms: 87.286883322 + -37 = 50.286883322 q = 50.286883322 Simplifying q = 50.286883322

Subproblem 2

q + 37 = -87.286883322 Simplifying q + 37 = -87.286883322 Reorder the terms: 37 + q = -87.286883322 Solving 37 + q = -87.286883322 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + q = -87.286883322 + -37 Combine like terms: 37 + -37 = 0 0 + q = -87.286883322 + -37 q = -87.286883322 + -37 Combine like terms: -87.286883322 + -37 = -124.286883322 q = -124.286883322 Simplifying q = -124.286883322

Solution

The solution to the problem is based on the solutions from the subproblems. q = {50.286883322, -124.286883322}

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