35-16q+2.25q^2=51

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Solution for 35-16q+2.25q^2=51 equation:


Simplifying
35 + -16q + 2.25q2 = 51

Solving
35 + -16q + 2.25q2 = 51

Solving for variable 'q'.

Reorder the terms:
35 + -51 + -16q + 2.25q2 = 51 + -51

Combine like terms: 35 + -51 = -16
-16 + -16q + 2.25q2 = 51 + -51

Combine like terms: 51 + -51 = 0
-16 + -16q + 2.25q2 = 0

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

Divide each side by '2.25'.
-7.111111111 + -7.111111111q + q2 = 0

Move the constant term to the right:

Add '7.111111111' to each side of the equation.
-7.111111111 + -7.111111111q + 7.111111111 + q2 = 0 + 7.111111111

Reorder the terms:
-7.111111111 + 7.111111111 + -7.111111111q + q2 = 0 + 7.111111111

Combine like terms: -7.111111111 + 7.111111111 = 0.000000000
0.000000000 + -7.111111111q + q2 = 0 + 7.111111111
-7.111111111q + q2 = 0 + 7.111111111

Combine like terms: 0 + 7.111111111 = 7.111111111
-7.111111111q + q2 = 7.111111111

The q term is -7.111111111q.  Take half its coefficient (-3.555555556).
Square it (12.64197531) and add it to both sides.

Add '12.64197531' to each side of the equation.
-7.111111111q + 12.64197531 + q2 = 7.111111111 + 12.64197531

Reorder the terms:
12.64197531 + -7.111111111q + q2 = 7.111111111 + 12.64197531

Combine like terms: 7.111111111 + 12.64197531 = 19.753086421
12.64197531 + -7.111111111q + q2 = 19.753086421

Factor a perfect square on the left side:
(q + -3.555555556)(q + -3.555555556) = 19.753086421

Calculate the square root of the right side: 4.444444445

Break this problem into two subproblems by setting 
(q + -3.555555556) equal to 4.444444445 and -4.444444445.

Subproblem 1

q + -3.555555556 = 4.444444445 Simplifying q + -3.555555556 = 4.444444445 Reorder the terms: -3.555555556 + q = 4.444444445 Solving -3.555555556 + q = 4.444444445 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + q = 4.444444445 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + q = 4.444444445 + 3.555555556 q = 4.444444445 + 3.555555556 Combine like terms: 4.444444445 + 3.555555556 = 8.000000001 q = 8.000000001 Simplifying q = 8.000000001

Subproblem 2

q + -3.555555556 = -4.444444445 Simplifying q + -3.555555556 = -4.444444445 Reorder the terms: -3.555555556 + q = -4.444444445 Solving -3.555555556 + q = -4.444444445 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + q = -4.444444445 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + q = -4.444444445 + 3.555555556 q = -4.444444445 + 3.555555556 Combine like terms: -4.444444445 + 3.555555556 = -0.888888889 q = -0.888888889 Simplifying q = -0.888888889

Solution

The solution to the problem is based on the solutions from the subproblems. q = {8.000000001, -0.888888889}

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