9x^2+5x-144=0

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Solution for 9x^2+5x-144=0 equation:


Simplifying
9x2 + 5x + -144 = 0

Reorder the terms:
-144 + 5x + 9x2 = 0

Solving
-144 + 5x + 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'.
-16 + 0.5555555556x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 0.5555555556x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 0.5555555556x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 0.5555555556x + x2 = 0 + 16
0.5555555556x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
0.5555555556x + x2 = 16

The x term is 0.5555555556x.  Take half its coefficient (0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
0.5555555556x + 0.07716049384 + x2 = 16 + 0.07716049384

Reorder the terms:
0.07716049384 + 0.5555555556x + x2 = 16 + 0.07716049384

Combine like terms: 16 + 0.07716049384 = 16.07716049384
0.07716049384 + 0.5555555556x + x2 = 16.07716049384

Factor a perfect square on the left side:
(x + 0.2777777778)(x + 0.2777777778) = 16.07716049384

Calculate the square root of the right side: 4.009633461

Break this problem into two subproblems by setting 
(x + 0.2777777778) equal to 4.009633461 and -4.009633461.

Subproblem 1

x + 0.2777777778 = 4.009633461 Simplifying x + 0.2777777778 = 4.009633461 Reorder the terms: 0.2777777778 + x = 4.009633461 Solving 0.2777777778 + x = 4.009633461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 4.009633461 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 4.009633461 + -0.2777777778 x = 4.009633461 + -0.2777777778 Combine like terms: 4.009633461 + -0.2777777778 = 3.7318556832 x = 3.7318556832 Simplifying x = 3.7318556832

Subproblem 2

x + 0.2777777778 = -4.009633461 Simplifying x + 0.2777777778 = -4.009633461 Reorder the terms: 0.2777777778 + x = -4.009633461 Solving 0.2777777778 + x = -4.009633461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -4.009633461 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -4.009633461 + -0.2777777778 x = -4.009633461 + -0.2777777778 Combine like terms: -4.009633461 + -0.2777777778 = -4.2874112388 x = -4.2874112388 Simplifying x = -4.2874112388

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.7318556832, -4.2874112388}

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