9x^2+3x-5=0

Simple and best practice solution for 9x^2+3x-5=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 9x^2+3x-5=0 equation: 


Simplifying
9x2 + 3x + -5 = 0

Reorder the terms:
-5 + 3x + 9x2 = 0

Solving
-5 + 3x + 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 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.5555555556' to each side of the equation.
-0.5555555556 + 0.3333333333x + 0.5555555556 + x2 = 0 + 0.5555555556

Reorder the terms:
-0.5555555556 + 0.5555555556 + 0.3333333333x + x2 = 0 + 0.5555555556

Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000
0.0000000000 + 0.3333333333x + x2 = 0 + 0.5555555556
0.3333333333x + x2 = 0 + 0.5555555556

Combine like terms: 0 + 0.5555555556 = 0.5555555556
0.3333333333x + x2 = 0.5555555556

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = 0.5555555556 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 0.5555555556 + 0.02777777779

Combine like terms: 0.5555555556 + 0.02777777779 = 0.58333333339
0.02777777779 + 0.3333333333x + x2 = 0.58333333339

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 0.58333333339

Calculate the square root of the right side: 0.763762616

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 0.763762616 and -0.763762616.


Subproblem 1
x + 0.1666666667 = 0.763762616

Simplifying
x + 0.1666666667 = 0.763762616

Reorder the terms:
0.1666666667 + x = 0.763762616

Solving
0.1666666667 + x = 0.763762616

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = 0.763762616 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = 0.763762616 + -0.1666666667
x = 0.763762616 + -0.1666666667

Combine like terms: 0.763762616 + -0.1666666667 = 0.5970959493
x = 0.5970959493

Simplifying
x = 0.5970959493


Subproblem 2
x + 0.1666666667 = -0.763762616

Simplifying
x + 0.1666666667 = -0.763762616

Reorder the terms:
0.1666666667 + x = -0.763762616

Solving
0.1666666667 + x = -0.763762616

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = -0.763762616 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = -0.763762616 + -0.1666666667
x = -0.763762616 + -0.1666666667

Combine like terms: -0.763762616 + -0.1666666667 = -0.9304292827
x = -0.9304292827

Simplifying
x = -0.9304292827


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5970959493, -0.9304292827}

See similar equations:

| 18x-10x=-63+11-5x | | U=5(7n+30)+9(n+1) | | 16=x^2-25 | | 6x-2=3x+7 | | 3x-3=13x-73 | | x^2-4+3=0 | | 6x+21=6x-69 | | 7x+31=4x-11 | | a^3b-ab^3= | | 5y-7+y+35=5y+40-3y | | 8a=96 | | 7w-5=8w+12 | | 120=5x(x+2) | | 7.5x=150 | | 144=6x(x+2) | | x-14=.85x | | 5x(x+2)=120 | | 17y+42=10y+7 | | (b+1)+9=2(3b-4)+b | | 44-7x=11x+22 | | 16x=100 | | 51=17h | | -54-9x=10x+22 | | 6-9x=86-23x | | 4x^2-x-3=-3 | | 2x+6=-30+7x | | 6+2=b | | 133-3x=5x+13 | | x-14=.7x | | x-14=.65x | | 3x+6=60-8x | | -16-4x=11-7x |

Equations solver categories