4x^2+13x-5=0

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


Simplifying
4x2 + 13x + -5 = 0

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

Solving
-5 + 13x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-1.25 + 3.25x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 3.25x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 3.25x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 3.25x + x2 = 0 + 1.25
3.25x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
3.25x + x2 = 1.25

The x term is 3.25x.  Take half its coefficient (1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
3.25x + 2.640625 + x2 = 1.25 + 2.640625

Reorder the terms:
2.640625 + 3.25x + x2 = 1.25 + 2.640625

Combine like terms: 1.25 + 2.640625 = 3.890625
2.640625 + 3.25x + x2 = 3.890625

Factor a perfect square on the left side:
(x + 1.625)(x + 1.625) = 3.890625

Calculate the square root of the right side: 1.97246673

Break this problem into two subproblems by setting 
(x + 1.625) equal to 1.97246673 and -1.97246673.

Subproblem 1

x + 1.625 = 1.97246673 Simplifying x + 1.625 = 1.97246673 Reorder the terms: 1.625 + x = 1.97246673 Solving 1.625 + x = 1.97246673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 1.97246673 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 1.97246673 + -1.625 x = 1.97246673 + -1.625 Combine like terms: 1.97246673 + -1.625 = 0.34746673 x = 0.34746673 Simplifying x = 0.34746673

Subproblem 2

x + 1.625 = -1.97246673 Simplifying x + 1.625 = -1.97246673 Reorder the terms: 1.625 + x = -1.97246673 Solving 1.625 + x = -1.97246673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -1.97246673 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -1.97246673 + -1.625 x = -1.97246673 + -1.625 Combine like terms: -1.97246673 + -1.625 = -3.59746673 x = -3.59746673 Simplifying x = -3.59746673

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.34746673, -3.59746673}

See similar equations:

| 8p+7-5p+6= | | 72=3x+5+4x+4 | | (x-4)/3-(2x+1)/7=(5x-1)/2 | | 2m-4=3m-9 | | f(x)=-4x^2+7x+2 | | x-5y-2=0 | | 78=24x-3-7x+4 | | 5x+1=5x+40 | | 12/48 | | 2=c/-8 | | 63=9+9x | | 36=1-7x | | 3/4g+8=5/4g | | z-6z=5z-1-z | | x/3+(3-x)/4=0 | | 5(v+2)+v=(v-1)+1 | | x-2/5=x/9 | | 7x+10y=19fory | | 5(t-5)+3t=4(2t+4)-12 | | -(8y+2)-(-7y-3)=-5 | | 9(v+2)=3v-18 | | 4w-6(6z-4w)=6z | | 51-2x=25x+21 | | 8=9u-6/8+6u+1/2 | | 15x+10=40x | | 12=8/4y+3/4-3/8y+1 | | -5x-7/2=4/5x-6/5 | | (3z+5)/7=(z+5)/4 | | 4x^2-47x+120=0 | | 5/3y-3=-7/2y+7/2 | | 320x^2-5y^2=0 | | -1/3y+7/2=-5/3y-1 |

Equations solver categories