9x^2+45x-5=

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Solution for 9x^2+45x-5= equation:


Simplifying
9x2 + 45x + -5 = 0

Reorder the terms:
-5 + 45x + 9x2 = 0

Solving
-5 + 45x + 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'.
-0.5555555556 + 5x + x2 = 0

Move the constant term to the right:

Add '0.5555555556' to each side of the equation.
-0.5555555556 + 5x + 0.5555555556 + x2 = 0 + 0.5555555556

Reorder the terms:
-0.5555555556 + 0.5555555556 + 5x + x2 = 0 + 0.5555555556

Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000
0.0000000000 + 5x + x2 = 0 + 0.5555555556
5x + x2 = 0 + 0.5555555556

Combine like terms: 0 + 0.5555555556 = 0.5555555556
5x + x2 = 0.5555555556

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 0.5555555556 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 0.5555555556 + 6.25

Combine like terms: 0.5555555556 + 6.25 = 6.8055555556
6.25 + 5x + x2 = 6.8055555556

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 6.8055555556

Calculate the square root of the right side: 2.608745974

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.608745974 and -2.608745974.

Subproblem 1

x + 2.5 = 2.608745974 Simplifying x + 2.5 = 2.608745974 Reorder the terms: 2.5 + x = 2.608745974 Solving 2.5 + x = 2.608745974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.608745974 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.608745974 + -2.5 x = 2.608745974 + -2.5 Combine like terms: 2.608745974 + -2.5 = 0.108745974 x = 0.108745974 Simplifying x = 0.108745974

Subproblem 2

x + 2.5 = -2.608745974 Simplifying x + 2.5 = -2.608745974 Reorder the terms: 2.5 + x = -2.608745974 Solving 2.5 + x = -2.608745974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.608745974 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.608745974 + -2.5 x = -2.608745974 + -2.5 Combine like terms: -2.608745974 + -2.5 = -5.108745974 x = -5.108745974 Simplifying x = -5.108745974

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.108745974, -5.108745974}

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