6x=2x^2+1

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


Simplifying
6x = 2x2 + 1

Reorder the terms:
6x = 1 + 2x2

Solving
6x = 1 + 2x2

Solving for variable 'x'.

Reorder the terms:
-1 + 6x + -2x2 = 1 + 2x2 + -1 + -2x2

Reorder the terms:
-1 + 6x + -2x2 = 1 + -1 + 2x2 + -2x2

Combine like terms: 1 + -1 = 0
-1 + 6x + -2x2 = 0 + 2x2 + -2x2
-1 + 6x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-1 + 6x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
0.5 + -3x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -3x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -3x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -3x + x2 = 0 + -0.5
-3x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-3x + x2 = -0.5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -0.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -0.5 + 2.25

Combine like terms: -0.5 + 2.25 = 1.75
2.25 + -3x + x2 = 1.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.322875656 and -1.322875656.

Subproblem 1

x + -1.5 = 1.322875656 Simplifying x + -1.5 = 1.322875656 Reorder the terms: -1.5 + x = 1.322875656 Solving -1.5 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.322875656 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.322875656 + 1.5 x = 1.322875656 + 1.5 Combine like terms: 1.322875656 + 1.5 = 2.822875656 x = 2.822875656 Simplifying x = 2.822875656

Subproblem 2

x + -1.5 = -1.322875656 Simplifying x + -1.5 = -1.322875656 Reorder the terms: -1.5 + x = -1.322875656 Solving -1.5 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.322875656 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.322875656 + 1.5 x = -1.322875656 + 1.5 Combine like terms: -1.322875656 + 1.5 = 0.177124344 x = 0.177124344 Simplifying x = 0.177124344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.822875656, 0.177124344}

See similar equations:

| 26x-10=-15 | | 2(x+9)=11x-18 | | 26x-10=15 | | 63=216 | | 2/1=x | | 2(1-6p)+8p=-30-8p | | 2(1-6p)+8p=30-8p | | f(x)=3(1.02)x | | -12-3n=-n-8(2n-2) | | -8x-36=4(-5-4x) | | 5x-6=-78-9x | | 2(x+(x-110))=1100 | | 6x^3y^3z+12x^2y^2z^3= | | -27-5x=4(-5-3x) | | 4x+13=-51 | | a-5=13-8a | | (2x-3x)2+(2x+3x)2=(81)2 | | 3v-11=v+3 | | (2x-3x)2+(2x+3x)2=81 | | 24x^2-48x+24= | | 13n-5=5n+8n | | 2r+10=r+4+4 | | 7+4x+8x=-5 | | -9=-8n-n | | 4x+0=81 | | 4=m+7-6 | | 0=1-4b+7 | | (2x-3x)+(2x+3x)=81 | | 6p+2p=24 | | 2x-3x+2x+3x=81 | | -(5y-8)-(5y+9)=20 | | -5x/10=-5 |

Equations solver categories