6x+9=2x^2

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


Simplifying
6x + 9 = 2x2

Reorder the terms:
9 + 6x = 2x2

Solving
9 + 6x = 2x2

Solving for variable 'x'.

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

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

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

Move the constant term to the right:

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

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

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -3x + x2 = 0 + 4.5
-3x + x2 = 0 + 4.5

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

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 = 4.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 4.5 + 2.25

Combine like terms: 4.5 + 2.25 = 6.75
2.25 + -3x + x2 = 6.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 6.75

Calculate the square root of the right side: 2.598076211

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.598076211 and -2.598076211.

Subproblem 1

x + -1.5 = 2.598076211 Simplifying x + -1.5 = 2.598076211 Reorder the terms: -1.5 + x = 2.598076211 Solving -1.5 + x = 2.598076211 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 = 2.598076211 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.598076211 + 1.5 x = 2.598076211 + 1.5 Combine like terms: 2.598076211 + 1.5 = 4.098076211 x = 4.098076211 Simplifying x = 4.098076211

Subproblem 2

x + -1.5 = -2.598076211 Simplifying x + -1.5 = -2.598076211 Reorder the terms: -1.5 + x = -2.598076211 Solving -1.5 + x = -2.598076211 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 = -2.598076211 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.598076211 + 1.5 x = -2.598076211 + 1.5 Combine like terms: -2.598076211 + 1.5 = -1.098076211 x = -1.098076211 Simplifying x = -1.098076211

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.098076211, -1.098076211}

See similar equations:

| 1.05x+5=.95+(8+.1x) | | 9x-7=x+3 | | -13=3(w-7)-5w | | k/3=-8 | | -7(x+1)-12-41=3 | | 12x+11y=-14 | | 2g=-8 | | 0.27(24)+0.03x=0.09(18x+x) | | 1.05x+5=.95+8+.1x | | X+x+3x+40=180 | | X+x+3x+40=189 | | X-7b=9 | | 7r^2-77r+168= | | (20x-15)-(6x+13)=(9x+37)-(5x-5) | | 0.4(a+2)=2-0.4 | | -x^4+12x^2-11=0 | | 382-h=327 | | 65=5+6g | | 7-y=7-5 | | x^2+60x-256=0 | | 3x+-7=x+41 | | 3x-7=x+33 | | 4/x+2/x=1 | | -6=-4+d | | 3(w-6)-7w= | | 7k^2=6k+1 | | 30b-12-64b+56=-24 | | 28-4/3h | | 2x+3=10x-53 | | 30b-12-64b+56=24 | | 3=d/4-3 | | -20-(-15)= |

Equations solver categories