3x^2+8x+3=0

Simple and best practice solution for 3x^2+8x+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 3x^2+8x+3=0 equation:


Simplifying
3x2 + 8x + 3 = 0

Reorder the terms:
3 + 8x + 3x2 = 0

Solving
3 + 8x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
1 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 2.666666667x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 2.666666667x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2.666666667x + x2 = 0 + -1
2.666666667x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
2.666666667x + x2 = -1

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = -1 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = -1 + 1.777777780

Combine like terms: -1 + 1.777777780 = 0.77777778
1.777777780 + 2.666666667x + x2 = 0.77777778

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 0.77777778

Calculate the square root of the right side: 0.881917105

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 0.881917105 and -0.881917105.

Subproblem 1

x + 1.333333334 = 0.881917105 Simplifying x + 1.333333334 = 0.881917105 Reorder the terms: 1.333333334 + x = 0.881917105 Solving 1.333333334 + x = 0.881917105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 0.881917105 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 0.881917105 + -1.333333334 x = 0.881917105 + -1.333333334 Combine like terms: 0.881917105 + -1.333333334 = -0.451416229 x = -0.451416229 Simplifying x = -0.451416229

Subproblem 2

x + 1.333333334 = -0.881917105 Simplifying x + 1.333333334 = -0.881917105 Reorder the terms: 1.333333334 + x = -0.881917105 Solving 1.333333334 + x = -0.881917105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -0.881917105 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -0.881917105 + -1.333333334 x = -0.881917105 + -1.333333334 Combine like terms: -0.881917105 + -1.333333334 = -2.215250439 x = -2.215250439 Simplifying x = -2.215250439

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.451416229, -2.215250439}

See similar equations:

| 3-7[7-(9y-4)]= | | 6x+5y=110000 | | 7=-4t | | 7(5y-4)+2(4y+6)= | | 7(5y-6)+2(4y+6)= | | 2-14=-8t+4t | | 5x^2+11x-66=0 | | 5(y*2-4)=-21y | | 6x^2+x=2 | | 6t*2=7 | | s*2-9=0 | | 4(6x-9)=3(12x-8) | | 6z-5=7z-7 | | 6(y+1)-5=7 | | 7-z=3+z+4-2z | | 2u=u-6 | | 8x-4=(2x+1) | | 2x^2+3y^2-30=0 | | 2w+3=7w+13 | | 4y^2+11y+7=5 | | 5y-8=3y+5 | | 4x-3x-7=6x | | 22-3(c-1)=-3c+25 | | 4k^2+6k-1=0 | | 4x-32=2x | | 2(n-1)=8n-3 | | 6x-1=25 | | 2y-x=8 | | -13(x+1)=-13x-13 | | 9x^2+49x+64=0 | | -5(a+1)=4(a+10) | | 4x-4=4x |

Equations solver categories