9x^2-113x-320=0

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Solution for 9x^2-113x-320=0 equation:


Simplifying
9x2 + -113x + -320 = 0

Reorder the terms:
-320 + -113x + 9x2 = 0

Solving
-320 + -113x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-35.55555556 + -12.55555556x + x2 = 0

Move the constant term to the right:

Add '35.55555556' to each side of the equation.
-35.55555556 + -12.55555556x + 35.55555556 + x2 = 0 + 35.55555556

Reorder the terms:
-35.55555556 + 35.55555556 + -12.55555556x + x2 = 0 + 35.55555556

Combine like terms: -35.55555556 + 35.55555556 = 0.00000000
0.00000000 + -12.55555556x + x2 = 0 + 35.55555556
-12.55555556x + x2 = 0 + 35.55555556

Combine like terms: 0 + 35.55555556 = 35.55555556
-12.55555556x + x2 = 35.55555556

The x term is -12.55555556x.  Take half its coefficient (-6.27777778).
Square it (39.41049386) and add it to both sides.

Add '39.41049386' to each side of the equation.
-12.55555556x + 39.41049386 + x2 = 35.55555556 + 39.41049386

Reorder the terms:
39.41049386 + -12.55555556x + x2 = 35.55555556 + 39.41049386

Combine like terms: 35.55555556 + 39.41049386 = 74.96604942
39.41049386 + -12.55555556x + x2 = 74.96604942

Factor a perfect square on the left side:
(x + -6.27777778)(x + -6.27777778) = 74.96604942

Calculate the square root of the right side: 8.658293678

Break this problem into two subproblems by setting 
(x + -6.27777778) equal to 8.658293678 and -8.658293678.

Subproblem 1

x + -6.27777778 = 8.658293678 Simplifying x + -6.27777778 = 8.658293678 Reorder the terms: -6.27777778 + x = 8.658293678 Solving -6.27777778 + x = 8.658293678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.27777778' to each side of the equation. -6.27777778 + 6.27777778 + x = 8.658293678 + 6.27777778 Combine like terms: -6.27777778 + 6.27777778 = 0.00000000 0.00000000 + x = 8.658293678 + 6.27777778 x = 8.658293678 + 6.27777778 Combine like terms: 8.658293678 + 6.27777778 = 14.936071458 x = 14.936071458 Simplifying x = 14.936071458

Subproblem 2

x + -6.27777778 = -8.658293678 Simplifying x + -6.27777778 = -8.658293678 Reorder the terms: -6.27777778 + x = -8.658293678 Solving -6.27777778 + x = -8.658293678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.27777778' to each side of the equation. -6.27777778 + 6.27777778 + x = -8.658293678 + 6.27777778 Combine like terms: -6.27777778 + 6.27777778 = 0.00000000 0.00000000 + x = -8.658293678 + 6.27777778 x = -8.658293678 + 6.27777778 Combine like terms: -8.658293678 + 6.27777778 = -2.380515898 x = -2.380515898 Simplifying x = -2.380515898

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.936071458, -2.380515898}

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