q^2+1.4q-0.51=0

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Solution for q^2+1.4q-0.51=0 equation: 


Simplifying
q2 + 1.4q + -0.51 = 0

Reorder the terms:
-0.51 + 1.4q + q2 = 0

Solving
-0.51 + 1.4q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '0.51' to each side of the equation.
-0.51 + 1.4q + 0.51 + q2 = 0 + 0.51

Reorder the terms:
-0.51 + 0.51 + 1.4q + q2 = 0 + 0.51

Combine like terms: -0.51 + 0.51 = 0.00
0.00 + 1.4q + q2 = 0 + 0.51
1.4q + q2 = 0 + 0.51

Combine like terms: 0 + 0.51 = 0.51
1.4q + q2 = 0.51

The q term is 1.4q.  Take half its coefficient (0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
1.4q + 0.49 + q2 = 0.51 + 0.49

Reorder the terms:
0.49 + 1.4q + q2 = 0.51 + 0.49

Combine like terms: 0.51 + 0.49 = 1
0.49 + 1.4q + q2 = 1

Factor a perfect square on the left side:
(q + 0.7)(q + 0.7) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(q + 0.7) equal to 1 and -1.


Subproblem 1
q + 0.7 = 1

Simplifying
q + 0.7 = 1

Reorder the terms:
0.7 + q = 1

Solving
0.7 + q = 1

Solving for variable 'q'.

Move all terms containing q to the left, all other terms to the right.

Add '-0.7' to each side of the equation.
0.7 + -0.7 + q = 1 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + q = 1 + -0.7
q = 1 + -0.7

Combine like terms: 1 + -0.7 = 0.3
q = 0.3

Simplifying
q = 0.3


Subproblem 2
q + 0.7 = -1

Simplifying
q + 0.7 = -1

Reorder the terms:
0.7 + q = -1

Solving
0.7 + q = -1

Solving for variable 'q'.

Move all terms containing q to the left, all other terms to the right.

Add '-0.7' to each side of the equation.
0.7 + -0.7 + q = -1 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + q = -1 + -0.7
q = -1 + -0.7

Combine like terms: -1 + -0.7 = -1.7
q = -1.7

Simplifying
q = -1.7


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.3, -1.7}

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