4u^2+9u+4=0

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


Simplifying
4u2 + 9u + 4 = 0

Reorder the terms:
4 + 9u + 4u2 = 0

Solving
4 + 9u + 4u2 = 0

Solving for variable 'u'.

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

Divide each side by '4'.
1 + 2.25u + u2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 2.25u + -1 + u2 = 0 + -1

Reorder the terms:
1 + -1 + 2.25u + u2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2.25u + u2 = 0 + -1
2.25u + u2 = 0 + -1

Combine like terms: 0 + -1 = -1
2.25u + u2 = -1

The u term is 2.25u.  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.
2.25u + 1.265625 + u2 = -1 + 1.265625

Reorder the terms:
1.265625 + 2.25u + u2 = -1 + 1.265625

Combine like terms: -1 + 1.265625 = 0.265625
1.265625 + 2.25u + u2 = 0.265625

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

Calculate the square root of the right side: 0.515388203

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


Subproblem 1
u + 1.125 = 0.515388203

Simplifying
u + 1.125 = 0.515388203

Reorder the terms:
1.125 + u = 0.515388203

Solving
1.125 + u = 0.515388203

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '-1.125' to each side of the equation.
1.125 + -1.125 + u = 0.515388203 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + u = 0.515388203 + -1.125
u = 0.515388203 + -1.125

Combine like terms: 0.515388203 + -1.125 = -0.609611797
u = -0.609611797

Simplifying
u = -0.609611797


Subproblem 2
u + 1.125 = -0.515388203

Simplifying
u + 1.125 = -0.515388203

Reorder the terms:
1.125 + u = -0.515388203

Solving
1.125 + u = -0.515388203

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '-1.125' to each side of the equation.
1.125 + -1.125 + u = -0.515388203 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + u = -0.515388203 + -1.125
u = -0.515388203 + -1.125

Combine like terms: -0.515388203 + -1.125 = -1.640388203
u = -1.640388203

Simplifying
u = -1.640388203


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

See similar equations:

| 8.3=x-6.1 | | -9=-5x+2x | | 8x-5=2(3x+1)+2x | | g^2-7=0 | | A/12=28 | | 3-m+3m=k | | 9/3=j/4 | | 1-4n-2n=7 | | 7.4x+3-9=6+7.4x | | 2u/u | | -12+x=12 | | t/8−3/4=9/16 | | 4/5×4/5 | | 6(y-1)=9y-24 | | -15/3=e | | O=p-6+8 | | A/22=-21 | | 6a-4=8a+6 | | -4=b^2-4b | | 3y=4x-9y | | n-8-5n=8 | | 4+8x+2x+6=8x+20 | | 40x-900=-15x+2400 | | 8=n/14 | | 18x-3-4=101 | | -25+y=-100 | | 2x+60=y | | g(-5)=5-4/5x | | -0.2+x= | | 3(x-9)+x-5=6(x+2)-2(x+22) | | -12=10 | | 4(2.5x-2)=10x-10+2 |

Equations solver categories