5q^2+2q=20

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Solution for 5q^2+2q=20 equation:


Simplifying
5q2 + 2q = 20

Reorder the terms:
2q + 5q2 = 20

Solving
2q + 5q2 = 20

Solving for variable 'q'.

Reorder the terms:
-20 + 2q + 5q2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 2q + 5q2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-4 + 0.4q + q2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 0.4q + 4 + q2 = 0 + 4

Reorder the terms:
-4 + 4 + 0.4q + q2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 0.4q + q2 = 0 + 4
0.4q + q2 = 0 + 4

Combine like terms: 0 + 4 = 4
0.4q + q2 = 4

The q term is 0.4q.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4q + 0.04 + q2 = 4 + 0.04

Reorder the terms:
0.04 + 0.4q + q2 = 4 + 0.04

Combine like terms: 4 + 0.04 = 4.04
0.04 + 0.4q + q2 = 4.04

Factor a perfect square on the left side:
(q + 0.2)(q + 0.2) = 4.04

Calculate the square root of the right side: 2.009975124

Break this problem into two subproblems by setting 
(q + 0.2) equal to 2.009975124 and -2.009975124.

Subproblem 1

q + 0.2 = 2.009975124 Simplifying q + 0.2 = 2.009975124 Reorder the terms: 0.2 + q = 2.009975124 Solving 0.2 + q = 2.009975124 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + q = 2.009975124 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + q = 2.009975124 + -0.2 q = 2.009975124 + -0.2 Combine like terms: 2.009975124 + -0.2 = 1.809975124 q = 1.809975124 Simplifying q = 1.809975124

Subproblem 2

q + 0.2 = -2.009975124 Simplifying q + 0.2 = -2.009975124 Reorder the terms: 0.2 + q = -2.009975124 Solving 0.2 + q = -2.009975124 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + q = -2.009975124 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + q = -2.009975124 + -0.2 q = -2.009975124 + -0.2 Combine like terms: -2.009975124 + -0.2 = -2.209975124 q = -2.209975124 Simplifying q = -2.209975124

Solution

The solution to the problem is based on the solutions from the subproblems. q = {1.809975124, -2.209975124}

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