0=4x^2-4x-1

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


Simplifying
0 = 4x2 + -4x + -1

Reorder the terms:
0 = -1 + -4x + 4x2

Solving
0 = -1 + -4x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 1 = 1
1 + 4x + -4x2 = -1 + -4x + 4x2 + 1 + 4x + -4x2

Reorder the terms:
1 + 4x + -4x2 = -1 + 1 + -4x + 4x + 4x2 + -4x2

Combine like terms: -1 + 1 = 0
1 + 4x + -4x2 = 0 + -4x + 4x + 4x2 + -4x2
1 + 4x + -4x2 = -4x + 4x + 4x2 + -4x2

Combine like terms: -4x + 4x = 0
1 + 4x + -4x2 = 0 + 4x2 + -4x2
1 + 4x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
1 + 4x + -4x2 = 0

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

Divide each side by '-4'.
-0.25 + -1x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1x + x2 = 0 + 0.25
-1x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1x + x2 = 0.25

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 = 0.25 + 0.25

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

Combine like terms: 0.25 + 0.25 = 0.5
0.25 + -1x + x2 = 0.5

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

Calculate the square root of the right side: 0.707106781

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

Subproblem 1

x + -0.5 = 0.707106781 Simplifying x + -0.5 = 0.707106781 Reorder the terms: -0.5 + x = 0.707106781 Solving -0.5 + x = 0.707106781 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 = 0.707106781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.707106781 + 0.5 x = 0.707106781 + 0.5 Combine like terms: 0.707106781 + 0.5 = 1.207106781 x = 1.207106781 Simplifying x = 1.207106781

Subproblem 2

x + -0.5 = -0.707106781 Simplifying x + -0.5 = -0.707106781 Reorder the terms: -0.5 + x = -0.707106781 Solving -0.5 + x = -0.707106781 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 = -0.707106781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.707106781 + 0.5 x = -0.707106781 + 0.5 Combine like terms: -0.707106781 + 0.5 = -0.207106781 x = -0.207106781 Simplifying x = -0.207106781

Solution

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

See similar equations:

| 15a^2b-35a^2= | | 5/9x6= | | (8-y)(5y+7)=0 | | 1/4=n/12 | | y=.25-logx | | 3x+5(-13x)=25 | | 10x-6+7x+3= | | 8x-1=10x-21 | | 2=8x-1 | | -5(10+3x)=-50 | | 2b+18+12b+20b=180 | | 2b+18+12b=180 | | 2b+18+12b=120 | | 2b+18=12b | | 2i*2i= | | 2x-(3x-8)+5x-6(x-1)=11 | | 12-(-6)/3= | | 0=x^2-14x-5880 | | 1+2+4=x | | -6√5/6 | | 4x^2-206x+1012=0 | | 3/4=20 | | 5x-20=x+14 | | 10-6X2+9/3 | | h=5k-6 | | 24x-14=10 | | 4x^2-140x+1200=0 | | -6(-8+2x)=-36 | | 6x-4=0+2x | | 25z^2-222=150z | | 2x/12=5/8 | | 7.5x-5x+24=0.5x+84 |

Equations solver categories