2x^2-21x-40=0

Simple and best practice solution for 2x^2-21x-40=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^2-21x-40=0 equation: 


Simplifying
2x2 + -21x + -40 = 0

Reorder the terms:
-40 + -21x + 2x2 = 0

Solving
-40 + -21x + 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'.
-20 + -10.5x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -10.5x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -10.5x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -10.5x + x2 = 0 + 20
-10.5x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-10.5x + x2 = 20

The x term is -10.5x.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5x + 27.5625 + x2 = 20 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = 20 + 27.5625

Combine like terms: 20 + 27.5625 = 47.5625
27.5625 + -10.5x + x2 = 47.5625

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 47.5625

Calculate the square root of the right side: 6.896557112

Break this problem into two subproblems by setting 
(x + -5.25) equal to 6.896557112 and -6.896557112.


Subproblem 1
x + -5.25 = 6.896557112

Simplifying
x + -5.25 = 6.896557112

Reorder the terms:
-5.25 + x = 6.896557112

Solving
-5.25 + x = 6.896557112

Solving for variable 'x'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + x = 6.896557112 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + x = 6.896557112 + 5.25
x = 6.896557112 + 5.25

Combine like terms: 6.896557112 + 5.25 = 12.146557112
x = 12.146557112

Simplifying
x = 12.146557112


Subproblem 2
x + -5.25 = -6.896557112

Simplifying
x + -5.25 = -6.896557112

Reorder the terms:
-5.25 + x = -6.896557112

Solving
-5.25 + x = -6.896557112

Solving for variable 'x'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + x = -6.896557112 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + x = -6.896557112 + 5.25
x = -6.896557112 + 5.25

Combine like terms: -6.896557112 + 5.25 = -1.646557112
x = -1.646557112

Simplifying
x = -1.646557112


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.146557112, -1.646557112}

See similar equations:

| -7n^2+4n-23=-10n^2-8 | | -1x+2y+4=0 | | 2x+12=-18 | | 6=e/4+2 | | 6=e/4+4 | | 6f+20=-2f-4 | | 44=4n | | 5(2x+6)= | | .60x-2=3.333 | | 0.5(-6)-8= | | 3+(5+2-4)2+12= | | 11+(-9)2= | | -8b^2+4b=-8 | | h=1/2(h+h) | | 3/4b=15 | | (-2)+-63+3= | | 3/4b+15 | | (-2)+-6+3= | | 6v^2-3=0 | | x+(x^1/2)=20 | | 1/2=4(5x-3) | | 3(-2)+-6+3= | | ln(x)+ln(6)= | | -8+3h=2h-10 | | 4n=(3/5) | | 6(2x+6)+17= | | 4x^4-11x^2-45=0 | | P=m+k+nform | | x+x^1/2=20 | | 8n^2+5=0 | | -116=-8+9v | | -4*0-6d=24 |

Equations solver categories