6x^2+20x+9=0

Simple and best practice solution for 6x^2+20x+9=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 6x^2+20x+9=0 equation:


Simplifying
6x2 + 20x + 9 = 0

Reorder the terms:
9 + 20x + 6x2 = 0

Solving
9 + 20x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
1.5 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 3.333333333x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 3.333333333x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 3.333333333x + x2 = 0 + -1.5
3.333333333x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
3.333333333x + x2 = -1.5

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = -1.5 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = -1.5 + 2.777777779

Combine like terms: -1.5 + 2.777777779 = 1.277777779
2.777777779 + 3.333333333x + x2 = 1.277777779

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 1.277777779

Calculate the square root of the right side: 1.130388331

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 1.130388331 and -1.130388331.

Subproblem 1

x + 1.666666667 = 1.130388331 Simplifying x + 1.666666667 = 1.130388331 Reorder the terms: 1.666666667 + x = 1.130388331 Solving 1.666666667 + x = 1.130388331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 1.130388331 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 1.130388331 + -1.666666667 x = 1.130388331 + -1.666666667 Combine like terms: 1.130388331 + -1.666666667 = -0.536278336 x = -0.536278336 Simplifying x = -0.536278336

Subproblem 2

x + 1.666666667 = -1.130388331 Simplifying x + 1.666666667 = -1.130388331 Reorder the terms: 1.666666667 + x = -1.130388331 Solving 1.666666667 + x = -1.130388331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -1.130388331 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -1.130388331 + -1.666666667 x = -1.130388331 + -1.666666667 Combine like terms: -1.130388331 + -1.666666667 = -2.797054998 x = -2.797054998 Simplifying x = -2.797054998

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.536278336, -2.797054998}

See similar equations:

| 185-5x=40x+15 | | 7a+9=3a | | -4n=22 | | 6x+7=31 | | 3(3-2x)-2(1-x)=10 | | 16+2x=-4(x+4) | | 12-m+5=m+7 | | 16a+10a=52 | | 4.1+10m=6.58 | | 6a-3a+2a=35 | | 9v-5=-95 | | 9x-7=8x-6 | | 40-5X=12X+6 | | x(x+10)=100 | | 21=6m | | 2/3x+4=-1/3x-3 | | 7y=4y+18 | | -(6+1)-(-5y-7)=6 | | 12/0.528 | | 5.7+g=13.2 | | -12+3+9= | | 20=4(x+12) | | (z^2)-z(3-2i)+5-i=0 | | 9x+6-2x=8 | | 6(2+3x)=11x+5 | | 8(4x+3)=-32+4x | | -3(8v+8)-4=36+8v | | 6x^2-31X+162=0 | | 4x^3+32x^2+64x=0 | | 4+6n=10+3n | | k/5+2=0 | | 47=-3+8d |

Equations solver categories