8q^2-6q=7q^2-8q+25

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Solution for 8q^2-6q=7q^2-8q+25 equation:


Simplifying
8q2 + -6q = 7q2 + -8q + 25

Reorder the terms:
-6q + 8q2 = 7q2 + -8q + 25

Reorder the terms:
-6q + 8q2 = 25 + -8q + 7q2

Solving
-6q + 8q2 = 25 + -8q + 7q2

Solving for variable 'q'.

Reorder the terms:
-25 + -6q + 8q + 8q2 + -7q2 = 25 + -8q + 7q2 + -25 + 8q + -7q2

Combine like terms: -6q + 8q = 2q
-25 + 2q + 8q2 + -7q2 = 25 + -8q + 7q2 + -25 + 8q + -7q2

Combine like terms: 8q2 + -7q2 = 1q2
-25 + 2q + 1q2 = 25 + -8q + 7q2 + -25 + 8q + -7q2

Reorder the terms:
-25 + 2q + 1q2 = 25 + -25 + -8q + 8q + 7q2 + -7q2

Combine like terms: 25 + -25 = 0
-25 + 2q + 1q2 = 0 + -8q + 8q + 7q2 + -7q2
-25 + 2q + 1q2 = -8q + 8q + 7q2 + -7q2

Combine like terms: -8q + 8q = 0
-25 + 2q + 1q2 = 0 + 7q2 + -7q2
-25 + 2q + 1q2 = 7q2 + -7q2

Combine like terms: 7q2 + -7q2 = 0
-25 + 2q + 1q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 2q + 25 + q2 = 0 + 25

Reorder the terms:
-25 + 25 + 2q + q2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 2q + q2 = 0 + 25
2q + q2 = 0 + 25

Combine like terms: 0 + 25 = 25
2q + q2 = 25

The q term is 2q.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2q + 1 + q2 = 25 + 1

Reorder the terms:
1 + 2q + q2 = 25 + 1

Combine like terms: 25 + 1 = 26
1 + 2q + q2 = 26

Factor a perfect square on the left side:
(q + 1)(q + 1) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(q + 1) equal to 5.099019514 and -5.099019514.

Subproblem 1

q + 1 = 5.099019514 Simplifying q + 1 = 5.099019514 Reorder the terms: 1 + q = 5.099019514 Solving 1 + q = 5.099019514 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q = 5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + q = 5.099019514 + -1 q = 5.099019514 + -1 Combine like terms: 5.099019514 + -1 = 4.099019514 q = 4.099019514 Simplifying q = 4.099019514

Subproblem 2

q + 1 = -5.099019514 Simplifying q + 1 = -5.099019514 Reorder the terms: 1 + q = -5.099019514 Solving 1 + q = -5.099019514 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q = -5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + q = -5.099019514 + -1 q = -5.099019514 + -1 Combine like terms: -5.099019514 + -1 = -6.099019514 q = -6.099019514 Simplifying q = -6.099019514

Solution

The solution to the problem is based on the solutions from the subproblems. q = {4.099019514, -6.099019514}

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