4x^2-x=1

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


Simplifying
4x2 + -1x = 1

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

Solving
-1x + 4x2 = 1

Solving for variable 'x'.

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

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

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

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

Move the constant term to the right:

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

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

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

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

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 0.25 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 0.25 + 0.015625

Combine like terms: 0.25 + 0.015625 = 0.265625
0.015625 + -0.25x + x2 = 0.265625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(x + -0.125) equal to 0.515388203 and -0.515388203.

Subproblem 1

x + -0.125 = 0.515388203 Simplifying x + -0.125 = 0.515388203 Reorder the terms: -0.125 + x = 0.515388203 Solving -0.125 + x = 0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.515388203 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.515388203 + 0.125 x = 0.515388203 + 0.125 Combine like terms: 0.515388203 + 0.125 = 0.640388203 x = 0.640388203 Simplifying x = 0.640388203

Subproblem 2

x + -0.125 = -0.515388203 Simplifying x + -0.125 = -0.515388203 Reorder the terms: -0.125 + x = -0.515388203 Solving -0.125 + x = -0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.515388203 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.515388203 + 0.125 x = -0.515388203 + 0.125 Combine like terms: -0.515388203 + 0.125 = -0.390388203 x = -0.390388203 Simplifying x = -0.390388203

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.640388203, -0.390388203}

See similar equations:

| 2z+6=z+8-2z | | f(-5)=-2.5-2 | | 12x^2-2=5x | | a^4+a^2-2=0 | | 0.375x+0.33x=5x+11+1.66 | | (6c-7d)-(3c+6d)= | | 2x^2+9x+19=0 | | 2x+30-5x=90 | | 1(r+10)=r-16 | | -[6z-(14z+3)]=3+(7z+8) | | -9+4r=4r-9 | | 5-36x=-60 | | 8x^3-49x^2-49x=0 | | (3x+7)+(6x+20)=90 | | 3-2x=2+3x | | z^2+9z=7 | | f(-5)=1-4(-5) | | 5-36x=60 | | 2n+4n+12=-6 | | 0.15x=0.05x+40 | | y^2-9= | | 8(2)x+7y=184 | | 7-5x+8+2x+4x-3=17 | | x^2+21x+35= | | 3/4=a | | 2(2x-4)=6x-20 | | 8b+11-3b=z+8-2x | | 2(7x+2)+12(x+1)=2 | | x^3+7x^2-x=0 | | 9b=4c | | 2r^2+19r+42=0 | | 5x-15=85 |

Equations solver categories