8x^2+38x+16=0

Simple and best practice solution for 8x^2+38x+16=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 8x^2+38x+16=0 equation: 


Simplifying
8x2 + 38x + 16 = 0

Reorder the terms:
16 + 38x + 8x2 = 0

Solving
16 + 38x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 19x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + 19x + 4x2)' equal to zero and attempt to solve:

Simplifying
8 + 19x + 4x2 = 0

Solving
8 + 19x + 4x2 = 0

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

Divide each side by '4'.
2 + 4.75x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 4.75x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 4.75x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 4.75x + x2 = 0 + -2
4.75x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
4.75x + x2 = -2

The x term is 4.75x.  Take half its coefficient (2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
4.75x + 5.640625 + x2 = -2 + 5.640625

Reorder the terms:
5.640625 + 4.75x + x2 = -2 + 5.640625

Combine like terms: -2 + 5.640625 = 3.640625
5.640625 + 4.75x + x2 = 3.640625

Factor a perfect square on the left side:
(x + 2.375)(x + 2.375) = 3.640625

Calculate the square root of the right side: 1.90804219

Break this problem into two subproblems by setting 
(x + 2.375) equal to 1.90804219 and -1.90804219.


Subproblem 1
x + 2.375 = 1.90804219

Simplifying
x + 2.375 = 1.90804219

Reorder the terms:
2.375 + x = 1.90804219

Solving
2.375 + x = 1.90804219

Solving for variable 'x'.

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

Add '-2.375' to each side of the equation.
2.375 + -2.375 + x = 1.90804219 + -2.375

Combine like terms: 2.375 + -2.375 = 0.000
0.000 + x = 1.90804219 + -2.375
x = 1.90804219 + -2.375

Combine like terms: 1.90804219 + -2.375 = -0.46695781
x = -0.46695781

Simplifying
x = -0.46695781


Subproblem 2
x + 2.375 = -1.90804219

Simplifying
x + 2.375 = -1.90804219

Reorder the terms:
2.375 + x = -1.90804219

Solving
2.375 + x = -1.90804219

Solving for variable 'x'.

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

Add '-2.375' to each side of the equation.
2.375 + -2.375 + x = -1.90804219 + -2.375

Combine like terms: 2.375 + -2.375 = 0.000
0.000 + x = -1.90804219 + -2.375
x = -1.90804219 + -2.375

Combine like terms: -1.90804219 + -2.375 = -4.28304219
x = -4.28304219

Simplifying
x = -4.28304219


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.46695781, -4.28304219}
Solution
x = {-0.46695781, -4.28304219}

See similar equations:

| 1-x^2=ax | | Y=in(x) | | 4x+3x=3x+4 | | 106+9x=4x+34 | | (6x1/4)^-1/2 | | (6x1/4)6-1/2 | | 7x+6=16+3x | | 3.6x=4.32 | | 3.6x=5.2 | | 2x*2x-1=3 | | (x+4)(x+4)=x^2+8x+16 | | y^2+y=96 | | 9z-1=6 | | (x-4)(x^2+4x+16)-x(x^2-6)=2 | | 5(2x-3)=(2x+3) | | 4y+3=3(y+2) | | 2x*2x-1=x+4 | | 25y^2+5y-6=0 | | 2x*2x-2x-1=-2 | | abc=7*ac | | 9x-12=3(x-6) | | 2x*2x-2x-1=3 | | -2x=4(x-6) | | 6-0.4=1.4 | | (2x*2x)-2x-1=3 | | 2(x-6)=-x | | x+0.06x=139.80 | | u/8=6 | | abcd+a+ab+abc=2012 | | 3-4a/5=-3a/4 | | y^2-2xy-4x+1=0 | | 4x=2(x-5) |

Equations solver categories