13x^2+5x-4=0

Simple and best practice solution for 13x^2+5x-4=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 13x^2+5x-4=0 equation: 


Simplifying
13x2 + 5x + -4 = 0

Reorder the terms:
-4 + 5x + 13x2 = 0

Solving
-4 + 5x + 13x2 = 0

Solving for variable 'x'.

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

Divide each side by '13'.
-0.3076923077 + 0.3846153846x + x2 = 0

Move the constant term to the right:

Add '0.3076923077' to each side of the equation.
-0.3076923077 + 0.3846153846x + 0.3076923077 + x2 = 0 + 0.3076923077

Reorder the terms:
-0.3076923077 + 0.3076923077 + 0.3846153846x + x2 = 0 + 0.3076923077

Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000
0.0000000000 + 0.3846153846x + x2 = 0 + 0.3076923077
0.3846153846x + x2 = 0 + 0.3076923077

Combine like terms: 0 + 0.3076923077 = 0.3076923077
0.3846153846x + x2 = 0.3076923077

The x term is 0.3846153846x.  Take half its coefficient (0.1923076923).
Square it (0.03698224852) and add it to both sides.

Add '0.03698224852' to each side of the equation.
0.3846153846x + 0.03698224852 + x2 = 0.3076923077 + 0.03698224852

Reorder the terms:
0.03698224852 + 0.3846153846x + x2 = 0.3076923077 + 0.03698224852

Combine like terms: 0.3076923077 + 0.03698224852 = 0.34467455622
0.03698224852 + 0.3846153846x + x2 = 0.34467455622

Factor a perfect square on the left side:
(x + 0.1923076923)(x + 0.1923076923) = 0.34467455622

Calculate the square root of the right side: 0.587089905

Break this problem into two subproblems by setting 
(x + 0.1923076923) equal to 0.587089905 and -0.587089905.


Subproblem 1
x + 0.1923076923 = 0.587089905

Simplifying
x + 0.1923076923 = 0.587089905

Reorder the terms:
0.1923076923 + x = 0.587089905

Solving
0.1923076923 + x = 0.587089905

Solving for variable 'x'.

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

Add '-0.1923076923' to each side of the equation.
0.1923076923 + -0.1923076923 + x = 0.587089905 + -0.1923076923

Combine like terms: 0.1923076923 + -0.1923076923 = 0.0000000000
0.0000000000 + x = 0.587089905 + -0.1923076923
x = 0.587089905 + -0.1923076923

Combine like terms: 0.587089905 + -0.1923076923 = 0.3947822127
x = 0.3947822127

Simplifying
x = 0.3947822127


Subproblem 2
x + 0.1923076923 = -0.587089905

Simplifying
x + 0.1923076923 = -0.587089905

Reorder the terms:
0.1923076923 + x = -0.587089905

Solving
0.1923076923 + x = -0.587089905

Solving for variable 'x'.

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

Add '-0.1923076923' to each side of the equation.
0.1923076923 + -0.1923076923 + x = -0.587089905 + -0.1923076923

Combine like terms: 0.1923076923 + -0.1923076923 = 0.0000000000
0.0000000000 + x = -0.587089905 + -0.1923076923
x = -0.587089905 + -0.1923076923

Combine like terms: -0.587089905 + -0.1923076923 = -0.7793975973
x = -0.7793975973

Simplifying
x = -0.7793975973


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3947822127, -0.7793975973}

See similar equations:

| 2(x+-1)+3+-2x=7 | | 125x*75y=45 | | 4x+12=84-2x | | 4(9x+8)+8=-6 | | -8c=-5c+21 | | -2y+y-5=5 | | 4s^4-16= | | 4x-(x-6)=12 | | y=5.50x+7 | | 20x^4-12x-2=0 | | 20x^4-12x-x=0 | | 8*r=2 | | 4x-x=2x+6 | | 4x+1=8x+9 | | -5y=-3x-6 | | -5y=-23x-6 | | (4-3)/2= | | 4*r=10 | | 27/8*5/2= | | p=-2x^2+13x-1 | | 4-3/2= | | 7a+2a+1= | | 18x=66 | | 6+-3(x+10)=-3 | | 10a+3b+7a+6b= | | 1/2x+3=57 | | 2/3x-4y=-1 | | x+3=57 | | 3-2g=15 | | 3x+25=7x-11 | | 5timesx=65 | | 3x+2+-5x=10 |

Equations solver categories