4q^2+9q+4=0

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


Simplifying
4q2 + 9q + 4 = 0

Reorder the terms:
4 + 9q + 4q2 = 0

Solving
4 + 9q + 4q2 = 0

Solving for variable 'q'.

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

Divide each side by '4'.
1 + 2.25q + q2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 2.25q + -1 + q2 = 0 + -1

Reorder the terms:
1 + -1 + 2.25q + q2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2.25q + q2 = 0 + -1
2.25q + q2 = 0 + -1

Combine like terms: 0 + -1 = -1
2.25q + q2 = -1

The q term is 2.25q.  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.
2.25q + 1.265625 + q2 = -1 + 1.265625

Reorder the terms:
1.265625 + 2.25q + q2 = -1 + 1.265625

Combine like terms: -1 + 1.265625 = 0.265625
1.265625 + 2.25q + q2 = 0.265625

Factor a perfect square on the left side:
(q + 1.125)(q + 1.125) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(q + 1.125) equal to 0.515388203 and -0.515388203.

Subproblem 1

q + 1.125 = 0.515388203 Simplifying q + 1.125 = 0.515388203 Reorder the terms: 1.125 + q = 0.515388203 Solving 1.125 + q = 0.515388203 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + q = 0.515388203 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + q = 0.515388203 + -1.125 q = 0.515388203 + -1.125 Combine like terms: 0.515388203 + -1.125 = -0.609611797 q = -0.609611797 Simplifying q = -0.609611797

Subproblem 2

q + 1.125 = -0.515388203 Simplifying q + 1.125 = -0.515388203 Reorder the terms: 1.125 + q = -0.515388203 Solving 1.125 + q = -0.515388203 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + q = -0.515388203 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + q = -0.515388203 + -1.125 q = -0.515388203 + -1.125 Combine like terms: -0.515388203 + -1.125 = -1.640388203 q = -1.640388203 Simplifying q = -1.640388203

Solution

The solution to the problem is based on the solutions from the subproblems. q = {-0.609611797, -1.640388203}

See similar equations:

| 7(3x+5)=11(x-9) | | -8t-12=-4t | | 9540=n-2(180) | | 0.8z-4.4=2 | | 3/7•63 | | 2y^2(5y+3)(y-2)=0 | | -4(5x+11)=138 | | 2l+2(40)=700 | | k^2-4K=29 | | 7+2p-2=9p+10-6p | | -2-13=-17 | | V=4/3*PI*2^3 | | z^2-24z=47 | | 4z-17=-9 | | 4x^2+9y^2-z^2=36 | | 49/4x1/3= | | 7x^6-4x^8= | | t^2+98=98 | | C(200)=.05(200)+5 | | 9g-14=g | | (9+y)(5y+3)=0 | | j^2-41=-16 | | k^2+48=0 | | g^2=121 | | -4+36=0 | | 5h-2+5(h+1)-2=0 | | (x+2.8)+(y+7)=121 | | 4v+4=0 | | h^2=1 | | 8+3t-1=8t+25-3t | | 7h-3+7(h+1)-3= | | 3w-8=17 |

Equations solver categories