q^2+8q=45

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Solution for q^2+8q=45 equation:


Simplifying
q2 + 8q = 45

Reorder the terms:
8q + q2 = 45

Solving
8q + q2 = 45

Solving for variable 'q'.

Reorder the terms:
-45 + 8q + q2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 8q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 8q + 45 + q2 = 0 + 45

Reorder the terms:
-45 + 45 + 8q + q2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 8q + q2 = 0 + 45
8q + q2 = 0 + 45

Combine like terms: 0 + 45 = 45
8q + q2 = 45

The q term is 8q.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8q + 16 + q2 = 45 + 16

Reorder the terms:
16 + 8q + q2 = 45 + 16

Combine like terms: 45 + 16 = 61
16 + 8q + q2 = 61

Factor a perfect square on the left side:
(q + 4)(q + 4) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(q + 4) equal to 7.810249676 and -7.810249676.

Subproblem 1

q + 4 = 7.810249676 Simplifying q + 4 = 7.810249676 Reorder the terms: 4 + q = 7.810249676 Solving 4 + q = 7.810249676 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + q = 7.810249676 + -4 Combine like terms: 4 + -4 = 0 0 + q = 7.810249676 + -4 q = 7.810249676 + -4 Combine like terms: 7.810249676 + -4 = 3.810249676 q = 3.810249676 Simplifying q = 3.810249676

Subproblem 2

q + 4 = -7.810249676 Simplifying q + 4 = -7.810249676 Reorder the terms: 4 + q = -7.810249676 Solving 4 + q = -7.810249676 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + q = -7.810249676 + -4 Combine like terms: 4 + -4 = 0 0 + q = -7.810249676 + -4 q = -7.810249676 + -4 Combine like terms: -7.810249676 + -4 = -11.810249676 q = -11.810249676 Simplifying q = -11.810249676

Solution

The solution to the problem is based on the solutions from the subproblems. q = {3.810249676, -11.810249676}

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