(2x^2)+9x+3=0

Simple and best practice solution for (2x^2)+9x+3=0 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)+9x+3=0 equation:


Simplifying
(2x2) + 9x + 3 = 0

Reorder the terms:
3 + 9x + (2x2) = 0

Solving
3 + 9x + (2x2) = 0

Solving for variable 'x'.

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

Divide each side by '2'.
1.5 + 4.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 4.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 4.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 4.5x + x2 = 0 + -1.5
4.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
4.5x + x2 = -1.5

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 = -1.5 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -1.5 + 5.0625

Combine like terms: -1.5 + 5.0625 = 3.5625
5.0625 + 4.5x + x2 = 3.5625

Factor a perfect square on the left side:
((x) + 2.25)((x) + 2.25) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
((x) + 2.25) equal to 1.887458609 and -1.887458609.

Subproblem 1

(x) + 2.25 = 1.887458609 Simplifying (x) + 2.25 = 1.887458609 x + 2.25 = 1.887458609 Reorder the terms: 2.25 + x = 1.887458609 Solving 2.25 + x = 1.887458609 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 = 1.887458609 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 1.887458609 + -2.25 x = 1.887458609 + -2.25 Combine like terms: 1.887458609 + -2.25 = -0.362541391 x = -0.362541391 Simplifying x = -0.362541391

Subproblem 2

(x) + 2.25 = -1.887458609 Simplifying (x) + 2.25 = -1.887458609 x + 2.25 = -1.887458609 Reorder the terms: 2.25 + x = -1.887458609 Solving 2.25 + x = -1.887458609 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 = -1.887458609 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -1.887458609 + -2.25 x = -1.887458609 + -2.25 Combine like terms: -1.887458609 + -2.25 = -4.137458609 x = -4.137458609 Simplifying x = -4.137458609

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.362541391, -4.137458609}

See similar equations:

| 19+3.5x=17+4.75x | | 3x-5=2y+5 | | 19x+3.5=17x+4.75 | | (12x^2)-20x+0=0 | | x=(ln(1/6))/3ln3 | | 3(2x-5)+5(4-x)=2(x+2) | | 12xy/6x | | 2x-6+2=2x-3 | | 4x-20+17=4x-3 | | 13x+30=3x+240 | | 3x^2=12+2y^2 | | 9-2(-3)+9= | | x-6=21+5x | | -4+3x=-8+9 | | 5*/=27 | | y=(2/3)3 | | 6x+111=-109-9x | | 11x^2-5x+81=0 | | y=(2/3)0 | | x^2+10x+19=-18 | | y=(2/3)-1 | | 2(5t-6)=30-2t | | y=(2/3)-4 | | 2/3×-10=-12 | | 5x+3=9x-13 | | 10=2(p-6)-4 | | 2x/x-2 | | 1+2x+6x^2= | | 11+9=12x-4 | | 2(x+3)+5=19 | | 2x^2+3x+6=3x^2-6x+8x | | 135x^2-24.81x-6.607=0 |

Equations solver categories