2x^2-9x-13=0

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


Simplifying
2x2 + -9x + -13 = 0

Reorder the terms:
-13 + -9x + 2x2 = 0

Solving
-13 + -9x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-6.5 + -4.5x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + -4.5x + 6.5 + x2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + -4.5x + x2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + -4.5x + x2 = 0 + 6.5
-4.5x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
-4.5x + x2 = 6.5

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 6.5 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 6.5 + 5.0625

Combine like terms: 6.5 + 5.0625 = 11.5625
5.0625 + -4.5x + x2 = 11.5625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 11.5625

Calculate the square root of the right side: 3.400367627

Break this problem into two subproblems by setting 
(x + -2.25) equal to 3.400367627 and -3.400367627.


Subproblem 1
x + -2.25 = 3.400367627

Simplifying
x + -2.25 = 3.400367627

Reorder the terms:
-2.25 + x = 3.400367627

Solving
-2.25 + x = 3.400367627

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 3.400367627 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 3.400367627 + 2.25
x = 3.400367627 + 2.25

Combine like terms: 3.400367627 + 2.25 = 5.650367627
x = 5.650367627

Simplifying
x = 5.650367627


Subproblem 2
x + -2.25 = -3.400367627

Simplifying
x + -2.25 = -3.400367627

Reorder the terms:
-2.25 + x = -3.400367627

Solving
-2.25 + x = -3.400367627

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -3.400367627 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -3.400367627 + 2.25
x = -3.400367627 + 2.25

Combine like terms: -3.400367627 + 2.25 = -1.150367627
x = -1.150367627

Simplifying
x = -1.150367627


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.650367627, -1.150367627}

See similar equations:

| -4(y-1)+1= | | 5x-2x+27= | | 3v+4v=21 | | 5x-(6-x)=9x-3(x+2) | | 2(2v+4)-6v= | | -15=3f | | 144=(2x+16)(x+3) | | 21+7x=4(4x+1)-1 | | 13.75+x=7.75 | | 9x-(3x+6)=7x-42 | | 7=-6(2)+b | | 14(27t-3758)=74t | | -5xy+6y+3xy^2= | | (8x+25)+5x=90 | | Y+6=-3(x-2) | | 2p=is-t | | 5z(3z+1)=3z+1 | | (-6*i)+(-6*i)= | | (X-5/2)=(X+2/3) | | (8x+25)+(5x)=180 | | (8x+25)=5x | | 12(x+5)=3(x-30) | | 2(t-1)-3(2t-1)=4-5(3t+1) | | 6p-2q=-5 | | (7x+6)=(3x+14) | | -2(-3x-4)=x-5+3 | | -8a-2(a-3)=22 | | -(n+1)+(2n-1)= | | 7x-2(3x-5)=26+1x | | (5x+12)=(8x-9) | | 3(x-4)=x+(-12)+2x | | (a+4)(7a+1)= |

Equations solver categories