4X^2+6X+9=25

Simple and best practice solution for 4X^2+6X+9=25 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 4X^2+6X+9=25 equation: 


Simplifying
4X2 + 6X + 9 = 25

Reorder the terms:
9 + 6X + 4X2 = 25

Solving
9 + 6X + 4X2 = 25

Solving for variable 'X'.

Reorder the terms:
9 + -25 + 6X + 4X2 = 25 + -25

Combine like terms: 9 + -25 = -16
-16 + 6X + 4X2 = 25 + -25

Combine like terms: 25 + -25 = 0
-16 + 6X + 4X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 3X + 2X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + 3X + 2X2)' equal to zero and attempt to solve:

Simplifying
-8 + 3X + 2X2 = 0

Solving
-8 + 3X + 2X2 = 0

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

Divide each side by '2'.
-4 + 1.5X + X2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 1.5X + 4 + X2 = 0 + 4

Reorder the terms:
-4 + 4 + 1.5X + X2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 1.5X + X2 = 0 + 4
1.5X + X2 = 0 + 4

Combine like terms: 0 + 4 = 4
1.5X + X2 = 4

The X term is 1.5X.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5X + 0.5625 + X2 = 4 + 0.5625

Reorder the terms:
0.5625 + 1.5X + X2 = 4 + 0.5625

Combine like terms: 4 + 0.5625 = 4.5625
0.5625 + 1.5X + X2 = 4.5625

Factor a perfect square on the left side:
(X + 0.75)(X + 0.75) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(X + 0.75) equal to 2.136000936 and -2.136000936.


Subproblem 1
X + 0.75 = 2.136000936

Simplifying
X + 0.75 = 2.136000936

Reorder the terms:
0.75 + X = 2.136000936

Solving
0.75 + X = 2.136000936

Solving for variable 'X'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + X = 2.136000936 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + X = 2.136000936 + -0.75
X = 2.136000936 + -0.75

Combine like terms: 2.136000936 + -0.75 = 1.386000936
X = 1.386000936

Simplifying
X = 1.386000936


Subproblem 2
X + 0.75 = -2.136000936

Simplifying
X + 0.75 = -2.136000936

Reorder the terms:
0.75 + X = -2.136000936

Solving
0.75 + X = -2.136000936

Solving for variable 'X'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + X = -2.136000936 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + X = -2.136000936 + -0.75
X = -2.136000936 + -0.75

Combine like terms: -2.136000936 + -0.75 = -2.886000936
X = -2.886000936

Simplifying
X = -2.886000936


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.386000936, -2.886000936}
Solution
X = {1.386000936, -2.886000936}

See similar equations:

| X+12y=48 | | 7-(-x+5)=10 | | -4x+3=-5x+6 | | 7a+2b^2= | | 1200-500d=24 | | 12y-4=-24 | | 6x-4(2-x)=11 | | 8p-12-3p-6= | | 9+3m=24 | | -27=-6u+3(u-8) | | 24x-6= | | c-50.00=0.80(c-100) | | 8(w+8)=-3w+9 | | 98-79= | | y=60x+90 | | y+4=95 | | 4n+2=2n+14 | | 19=-7v+5(v+5) | | 2(2-2r)=3(2-2r) | | C-50=0.8(c-100) | | 90=k(60) | | 5(4x-2)+4=-4 | | -10v+12= | | -8+6x=5x-5 | | x^2-3ix+5=0 | | 450=0.8(c-100) | | -6x+18=-5 | | 8b-(4b)= | | 5n^2+15n-200=0 | | 3d+9= | | -4a+4+5a=12-21 | | 90=x(60) |

Equations solver categories