4x^2-4x-11=0

Simple and best practice solution for 4x^2-4x-11=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^2-4x-11=0 equation:


Simplifying
4x2 + -4x + -11 = 0

Reorder the terms:
-11 + -4x + 4x2 = 0

Solving
-11 + -4x + 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'.
-2.75 + -1x + x2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + -1x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + -1x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + -1x + x2 = 0 + 2.75
-1x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
-1x + x2 = 2.75

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 2.75 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 2.75 + 0.25

Combine like terms: 2.75 + 0.25 = 3
0.25 + -1x + x2 = 3

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.732050808 and -1.732050808.

Subproblem 1

x + -0.5 = 1.732050808 Simplifying x + -0.5 = 1.732050808 Reorder the terms: -0.5 + x = 1.732050808 Solving -0.5 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.732050808 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.732050808 + 0.5 x = 1.732050808 + 0.5 Combine like terms: 1.732050808 + 0.5 = 2.232050808 x = 2.232050808 Simplifying x = 2.232050808

Subproblem 2

x + -0.5 = -1.732050808 Simplifying x + -0.5 = -1.732050808 Reorder the terms: -0.5 + x = -1.732050808 Solving -0.5 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.732050808 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.732050808 + 0.5 x = -1.732050808 + 0.5 Combine like terms: -1.732050808 + 0.5 = -1.232050808 x = -1.232050808 Simplifying x = -1.232050808

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.232050808, -1.232050808}

See similar equations:

| 4a-9a= | | 4a-9a= | | 3=-16t^2+50t+2 | | 91=5c-c-(16)+8c | | 6x^2+26x+8=0 | | 4+2g=-6 | | -6x+10+10x=18 | | 25x^2-40x+16=0 | | -6+10+10x=18 | | m^2-8m+14=0 | | (10x^5)-(4x^4)=0 | | 2(x+3)=32 | | 2(x-3)=16 | | 4x^2-4x+11=0 | | 3c+c=6c | | m+9.5=12.4 | | P(n)=3n+3 | | 132=20+.5q | | 2x=38 | | 6+5x=2(x+6) | | X+3=22 | | x^4-32x^2+256=0 | | -2x-7=9 | | 4x^2-21x=0 | | 3(2x+-3)-3x+12=27 | | 4x^2-33x-27=0 | | 2x+10x=600 | | -9x+5=32 | | 2x+10x=20 | | 2x+3x-5x=100 | | 5x-8y=11 | | 3(2x-3)-3x+23=27 |

Equations solver categories