20x^2+13x-9=0

Simple and best practice solution for 20x^2+13x-9=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 20x^2+13x-9=0 equation: 


Simplifying
20x2 + 13x + -9 = 0

Reorder the terms:
-9 + 13x + 20x2 = 0

Solving
-9 + 13x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
-0.45 + 0.65x + x2 = 0

Move the constant term to the right:

Add '0.45' to each side of the equation.
-0.45 + 0.65x + 0.45 + x2 = 0 + 0.45

Reorder the terms:
-0.45 + 0.45 + 0.65x + x2 = 0 + 0.45

Combine like terms: -0.45 + 0.45 = 0.00
0.00 + 0.65x + x2 = 0 + 0.45
0.65x + x2 = 0 + 0.45

Combine like terms: 0 + 0.45 = 0.45
0.65x + x2 = 0.45

The x term is 0.65x.  Take half its coefficient (0.325).
Square it (0.105625) and add it to both sides.

Add '0.105625' to each side of the equation.
0.65x + 0.105625 + x2 = 0.45 + 0.105625

Reorder the terms:
0.105625 + 0.65x + x2 = 0.45 + 0.105625

Combine like terms: 0.45 + 0.105625 = 0.555625
0.105625 + 0.65x + x2 = 0.555625

Factor a perfect square on the left side:
(x + 0.325)(x + 0.325) = 0.555625

Calculate the square root of the right side: 0.745402576

Break this problem into two subproblems by setting 
(x + 0.325) equal to 0.745402576 and -0.745402576.


Subproblem 1
x + 0.325 = 0.745402576

Simplifying
x + 0.325 = 0.745402576

Reorder the terms:
0.325 + x = 0.745402576

Solving
0.325 + x = 0.745402576

Solving for variable 'x'.

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

Add '-0.325' to each side of the equation.
0.325 + -0.325 + x = 0.745402576 + -0.325

Combine like terms: 0.325 + -0.325 = 0.000
0.000 + x = 0.745402576 + -0.325
x = 0.745402576 + -0.325

Combine like terms: 0.745402576 + -0.325 = 0.420402576
x = 0.420402576

Simplifying
x = 0.420402576


Subproblem 2
x + 0.325 = -0.745402576

Simplifying
x + 0.325 = -0.745402576

Reorder the terms:
0.325 + x = -0.745402576

Solving
0.325 + x = -0.745402576

Solving for variable 'x'.

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

Add '-0.325' to each side of the equation.
0.325 + -0.325 + x = -0.745402576 + -0.325

Combine like terms: 0.325 + -0.325 = 0.000
0.000 + x = -0.745402576 + -0.325
x = -0.745402576 + -0.325

Combine like terms: -0.745402576 + -0.325 = -1.070402576
x = -1.070402576

Simplifying
x = -1.070402576


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.420402576, -1.070402576}

See similar equations:

| 7a+2=42-3a | | 5(2k-3)=-2k+9 | | 2x^5-72x=0 | | 5+49x=28x+41 | | log[5](2x+5)-log[5](x+5)=1 | | 7-3F=2 | | 7x+76=2x+36 | | 3y^2+20y+25=0 | | -3+6x=12 | | 9t^3+15t^2+t-6=(t+3)(t-2)-3t | | .6x+2=17 | | 5n+11= | | 32=2x+8 | | -11k+6=3k-8 | | 2n-6+21=5 | | x^2y+6xy^2= | | 4a+6(6+8)= | | 9x-4(x+2)-6=5 | | 4g-3h+5g-2h= | | 175=2.76x+4.05 | | 6(4y-1)=42 | | g^12-343= | | 73=3.25x-5 | | 12-4(6x-3)= | | 2x-9-3r=4 | | 3=2t^2+t | | z+1=z-9 | | 3m^2+9m-7= | | 22x-11-13x=3(3x-5)+4 | | 3r+1=r+13 | | 18-6x=12-7x | | 65.57=0.09x+2.57 |

Equations solver categories