4x^2=6x-1

Simple and best practice solution for 4x^2=6x-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=6x-1 equation:


Simplifying
4x2 = 6x + -1

Reorder the terms:
4x2 = -1 + 6x

Solving
4x2 = -1 + 6x

Solving for variable 'x'.

Reorder the terms:
1 + -6x + 4x2 = -1 + 6x + 1 + -6x

Reorder the terms:
1 + -6x + 4x2 = -1 + 1 + 6x + -6x

Combine like terms: -1 + 1 = 0
1 + -6x + 4x2 = 0 + 6x + -6x
1 + -6x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
1 + -6x + 4x2 = 0

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

Divide each side by '4'.
0.25 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1.5x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1.5x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1.5x + x2 = 0 + -0.25
-1.5x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1.5x + x2 = -0.25

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -0.25 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -0.25 + 0.5625

Combine like terms: -0.25 + 0.5625 = 0.3125
0.5625 + -1.5x + x2 = 0.3125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(x + -0.75) equal to 0.559016994 and -0.559016994.

Subproblem 1

x + -0.75 = 0.559016994 Simplifying x + -0.75 = 0.559016994 Reorder the terms: -0.75 + x = 0.559016994 Solving -0.75 + x = 0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.559016994 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.559016994 + 0.75 x = 0.559016994 + 0.75 Combine like terms: 0.559016994 + 0.75 = 1.309016994 x = 1.309016994 Simplifying x = 1.309016994

Subproblem 2

x + -0.75 = -0.559016994 Simplifying x + -0.75 = -0.559016994 Reorder the terms: -0.75 + x = -0.559016994 Solving -0.75 + x = -0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.559016994 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.559016994 + 0.75 x = -0.559016994 + 0.75 Combine like terms: -0.559016994 + 0.75 = 0.190983006 x = 0.190983006 Simplifying x = 0.190983006

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.309016994, 0.190983006}

See similar equations:

| s^2-12s=0 | | 25t^2+36=60t | | 2(g-15)=120 | | 25r^2+64=80r | | 3y-2(y+3)=0 | | 2b-3+b-4= | | 4a-6+9a-5= | | (x+3)(3x-1)=10x-2x^2 | | 3n-9-n= | | 1-7a-7-8a= | | r-6-2= | | 1-5v-8v= | | -[6z-(13z+3)]=3+(6z+8) | | 10x-12=4x+6 | | 7x^2+25x+2=0 | | 3+2x+6=-12 | | r^4-144= | | -0.3x+9=0.25x+3.5 | | n^2-13n+72=0 | | 2[w-(2w+11)+7]=2(w+4) | | 936=12q | | 4u+10=7(u+4) | | g+80=623 | | -28=-5x+2(x-8) | | (-3v^3/w^2) | | 18=-2x+3(-2x-18) | | 4(w+3)+6w=32 | | 180s^2-245= | | b/-26=-19 | | (-3v^3/w^2)^2 | | -20=2(u-2)-4u | | 5x^2+16x=20-5x |

Equations solver categories