4j^2+9j+3=0

Simple and best practice solution for 4j^2+9j+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 4j^2+9j+3=0 equation:


Simplifying
4j2 + 9j + 3 = 0

Reorder the terms:
3 + 9j + 4j2 = 0

Solving
3 + 9j + 4j2 = 0

Solving for variable 'j'.

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

Divide each side by '4'.
0.75 + 2.25j + j2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 2.25j + -0.75 + j2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 2.25j + j2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 2.25j + j2 = 0 + -0.75
2.25j + j2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
2.25j + j2 = -0.75

The j term is 2.25j.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25j + 1.265625 + j2 = -0.75 + 1.265625

Reorder the terms:
1.265625 + 2.25j + j2 = -0.75 + 1.265625

Combine like terms: -0.75 + 1.265625 = 0.515625
1.265625 + 2.25j + j2 = 0.515625

Factor a perfect square on the left side:
(j + 1.125)(j + 1.125) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(j + 1.125) equal to 0.718070331 and -0.718070331.

Subproblem 1

j + 1.125 = 0.718070331 Simplifying j + 1.125 = 0.718070331 Reorder the terms: 1.125 + j = 0.718070331 Solving 1.125 + j = 0.718070331 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + j = 0.718070331 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + j = 0.718070331 + -1.125 j = 0.718070331 + -1.125 Combine like terms: 0.718070331 + -1.125 = -0.406929669 j = -0.406929669 Simplifying j = -0.406929669

Subproblem 2

j + 1.125 = -0.718070331 Simplifying j + 1.125 = -0.718070331 Reorder the terms: 1.125 + j = -0.718070331 Solving 1.125 + j = -0.718070331 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + j = -0.718070331 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + j = -0.718070331 + -1.125 j = -0.718070331 + -1.125 Combine like terms: -0.718070331 + -1.125 = -1.843070331 j = -1.843070331 Simplifying j = -1.843070331

Solution

The solution to the problem is based on the solutions from the subproblems. j = {-0.406929669, -1.843070331}

See similar equations:

| k/5+81.8=47.2 | | 2c-4=17+5c | | 2x-5/3x-3=1/2 | | 8k+3=2k+33 | | 4x^2+4y^2=27 | | -4.2x+31=-53 | | 3x-3-3=24 | | 5.5x-5=-60 | | 5v-6=-21 | | 13=3u+7 | | 30=9.6x | | 6x(360/4) | | 7w^2-3w-9=0 | | 5(s+2t)+2(3s-t)= | | -4+3x=5x | | 0.66x=5 | | 83.7(-723.7)= | | X^2+8=-30 | | 7k^2-3k-5=0 | | a^4-a^3-3a^2+5a-2=0 | | 8d^2-7d-3=0 | | x^2+2y^2-8y-6x-9=0 | | x^10-100=0 | | (3x+14)+(2x-4)=60 | | 25/100=x/4260 | | 5y-10+y+60=6y+50-3y | | y=-(x+3)(2x-7) | | -24a^5b^3/21a^2b | | 6+13s-4=7s+57-5s | | 20(x)=14(0.5) | | 12y-4y+3= | | 2c^2-16c+30=0 |

Equations solver categories