2x^2+6=9x

Simple and best practice solution for 2x^2+6=9x 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 2x^2+6=9x equation:


Simplifying
2x2 + 6 = 9x

Reorder the terms:
6 + 2x2 = 9x

Solving
6 + 2x2 = 9x

Solving for variable 'x'.

Reorder the terms:
6 + -9x + 2x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
6 + -9x + 2x2 = 0

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

Divide each side by '2'.
3 + -4.5x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -4.5x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -4.5x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4.5x + x2 = 0 + -3
-4.5x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-4.5x + x2 = -3

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = -3 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = -3 + 5.0625

Combine like terms: -3 + 5.0625 = 2.0625
5.0625 + -4.5x + x2 = 2.0625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x + -2.25) equal to 1.436140662 and -1.436140662.

Subproblem 1

x + -2.25 = 1.436140662 Simplifying x + -2.25 = 1.436140662 Reorder the terms: -2.25 + x = 1.436140662 Solving -2.25 + x = 1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 1.436140662 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.436140662 + 2.25 x = 1.436140662 + 2.25 Combine like terms: 1.436140662 + 2.25 = 3.686140662 x = 3.686140662 Simplifying x = 3.686140662

Subproblem 2

x + -2.25 = -1.436140662 Simplifying x + -2.25 = -1.436140662 Reorder the terms: -2.25 + x = -1.436140662 Solving -2.25 + x = -1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -1.436140662 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.436140662 + 2.25 x = -1.436140662 + 2.25 Combine like terms: -1.436140662 + 2.25 = 0.813859338 x = 0.813859338 Simplifying x = 0.813859338

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.686140662, 0.813859338}

See similar equations:

| 200+10m=400 | | 7+5x+4x=8 | | 175n^2-448=0 | | 4x/20 | | f(n+1)=f(n)-5 | | 12.75x=1.5x | | 5w^3+5w^2-130w+120=0 | | -7/16×-16-26=-19 | | 1/2=1/6d | | 12-1/2r=2-1/2 | | -5+3x+3x=1 | | -7/16(-16-26)=-19 | | 20x+15=500-10x | | 8cos(x)-4=0 | | z=3+(5x-14)i | | 2500+150m=10000 | | 10m(m+3)=13m-3 | | 17x=2x | | 2b+5a-6b-a= | | -27a+70-40a-8= | | 12-2w=42 | | 50-5d=15 | | 2(x-3)-1=7x | | 5u-12=53 | | -(4x-8y)= | | 11-4y=32 | | 21-(2t+17)=-7-3t | | (x+9)(x-9)=-21 | | 6m+7(7m+9)=equation | | 30-49= | | 3M-8m-7+2= | | 16=6x+x+9 |

Equations solver categories