4a^2-4a-1=0

Simple and best practice solution for 4a^2-4a-1=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 4a^2-4a-1=0 equation:


Simplifying
4a2 + -4a + -1 = 0

Reorder the terms:
-1 + -4a + 4a2 = 0

Solving
-1 + -4a + 4a2 = 0

Solving for variable 'a'.

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

Divide each side by '4'.
-0.25 + -1a + a2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1a + 0.25 + a2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1a + a2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1a + a2 = 0 + 0.25
-1a + a2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1a + a2 = 0.25

The a term is -1a.  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.
-1a + 0.25 + a2 = 0.25 + 0.25

Reorder the terms:
0.25 + -1a + a2 = 0.25 + 0.25

Combine like terms: 0.25 + 0.25 = 0.5
0.25 + -1a + a2 = 0.5

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

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(a + -0.5) equal to 0.707106781 and -0.707106781.

Subproblem 1

a + -0.5 = 0.707106781 Simplifying a + -0.5 = 0.707106781 Reorder the terms: -0.5 + a = 0.707106781 Solving -0.5 + a = 0.707106781 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = 0.707106781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 0.707106781 + 0.5 a = 0.707106781 + 0.5 Combine like terms: 0.707106781 + 0.5 = 1.207106781 a = 1.207106781 Simplifying a = 1.207106781

Subproblem 2

a + -0.5 = -0.707106781 Simplifying a + -0.5 = -0.707106781 Reorder the terms: -0.5 + a = -0.707106781 Solving -0.5 + a = -0.707106781 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = -0.707106781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -0.707106781 + 0.5 a = -0.707106781 + 0.5 Combine like terms: -0.707106781 + 0.5 = -0.207106781 a = -0.207106781 Simplifying a = -0.207106781

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.207106781, -0.207106781}

See similar equations:

| 1,512.50/27= | | 2y+0y=10 | | 4(2x-1)=0 | | 37/60-1/3 | | (6-1)-(-12+2)= | | 7(x-8y)= | | -2.4+c=7.2 | | 7(c-8y)= | | -2/w-10=6/4+2w | | 2/3x+6=14 | | 1100+600+6x=650+500+8x | | -10-(8-10)= | | 16-(x^2-2xy+y^2)=0 | | 1/4+9/20 | | 1/3(6y-9)=-2+13 | | 25+10=15 | | -16-6(3)=2(8(3)-7) | | (-22+33)-11= | | 13/15-1/5 | | 2=11/4+1/8x | | -4+2y=2 | | 1/2+1/15 | | -16t^2+56t-40=0 | | 2-(1-9)= | | 3(1-d)=2-(2d-4) | | 41/60-1/5 | | 30+(3-5)= | | -6m+17=2m+1 | | x+7=70 | | n-0.13=-0.58 | | -3+16= | | 60-4x-x^2=0 |

Equations solver categories