4x^2-40x-84=0

Simple and best practice solution for 4x^2-40x-84=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^2-40x-84=0 equation: 


Simplifying
4x2 + -40x + -84 = 0

Reorder the terms:
-84 + -40x + 4x2 = 0

Solving
-84 + -40x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-21 + -10x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-21 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
-21 + -10x + x2 = 0

Solving
-21 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -10x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + -10x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -10x + x2 = 0 + 21
-10x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
-10x + x2 = 21

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 21 + 25

Reorder the terms:
25 + -10x + x2 = 21 + 25

Combine like terms: 21 + 25 = 46
25 + -10x + x2 = 46

Factor a perfect square on the left side:
(x + -5)(x + -5) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x + -5) equal to 6.782329983 and -6.782329983.


Subproblem 1
x + -5 = 6.782329983

Simplifying
x + -5 = 6.782329983

Reorder the terms:
-5 + x = 6.782329983

Solving
-5 + x = 6.782329983

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 6.782329983 + 5

Combine like terms: -5 + 5 = 0
0 + x = 6.782329983 + 5
x = 6.782329983 + 5

Combine like terms: 6.782329983 + 5 = 11.782329983
x = 11.782329983

Simplifying
x = 11.782329983


Subproblem 2
x + -5 = -6.782329983

Simplifying
x + -5 = -6.782329983

Reorder the terms:
-5 + x = -6.782329983

Solving
-5 + x = -6.782329983

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -6.782329983 + 5

Combine like terms: -5 + 5 = 0
0 + x = -6.782329983 + 5
x = -6.782329983 + 5

Combine like terms: -6.782329983 + 5 = -1.782329983
x = -1.782329983

Simplifying
x = -1.782329983


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.782329983, -1.782329983}
Solution
x = {11.782329983, -1.782329983}

See similar equations:

| -12x-21=9-11x | | -0.6666666666666666666666666666666666666667x+2.3=6x-11 | | 1.5x-2=-x+13 | | (b+2)(b-2)= | | -4v/5=8 | | lne^3=3 | | -7(9+2w)= | | x+10000=1.5x+5000 | | -5/7x=30 | | y=1/3x^2-4 | | 10x+17=-24+10 | | 3(2(2.9)-0.3)=19.4-(2.9) | | 5x-138=-2x+58 | | 5x+3(5x-10)=230 | | 11-5(6x-20)=81 | | bx=ab+bc | | 1/3x1/5 | | 3x+-20=5x+-130 | | 3x+b=13b | | 0.4x+0.5=-1.9-0.8x | | -15/8=-5y | | x+(x*.07)=90.42 | | -16=-4/3w | | 5d=(-35) | | 2(3x-4)-7=3x+1+1 | | 3-2p=-7 | | 5x^2-16x=45 | | 7.50x=12.50x | | -8x-63=29-4x | | 1m+3d=2.55 | | 7(2k+1)= | | 56n-24t= |

Equations solver categories