q^2+24q-37=0

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Solution for q^2+24q-37=0 equation:


Simplifying
q2 + 24q + -37 = 0

Reorder the terms:
-37 + 24q + q2 = 0

Solving
-37 + 24q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 24q + 37 + q2 = 0 + 37

Reorder the terms:
-37 + 37 + 24q + q2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 24q + q2 = 0 + 37
24q + q2 = 0 + 37

Combine like terms: 0 + 37 = 37
24q + q2 = 37

The q term is 24q.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24q + 144 + q2 = 37 + 144

Reorder the terms:
144 + 24q + q2 = 37 + 144

Combine like terms: 37 + 144 = 181
144 + 24q + q2 = 181

Factor a perfect square on the left side:
(q + 12)(q + 12) = 181

Calculate the square root of the right side: 13.453624047

Break this problem into two subproblems by setting 
(q + 12) equal to 13.453624047 and -13.453624047.

Subproblem 1

q + 12 = 13.453624047 Simplifying q + 12 = 13.453624047 Reorder the terms: 12 + q = 13.453624047 Solving 12 + q = 13.453624047 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + q = 13.453624047 + -12 Combine like terms: 12 + -12 = 0 0 + q = 13.453624047 + -12 q = 13.453624047 + -12 Combine like terms: 13.453624047 + -12 = 1.453624047 q = 1.453624047 Simplifying q = 1.453624047

Subproblem 2

q + 12 = -13.453624047 Simplifying q + 12 = -13.453624047 Reorder the terms: 12 + q = -13.453624047 Solving 12 + q = -13.453624047 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + q = -13.453624047 + -12 Combine like terms: 12 + -12 = 0 0 + q = -13.453624047 + -12 q = -13.453624047 + -12 Combine like terms: -13.453624047 + -12 = -25.453624047 q = -25.453624047 Simplifying q = -25.453624047

Solution

The solution to the problem is based on the solutions from the subproblems. q = {1.453624047, -25.453624047}

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