7x(7+x)=8(14)

Simple and best practice solution for 7x(7+x)=8(14) 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 7x(7+x)=8(14) equation: 


Simplifying
7x(7 + x) = 8(14)
(7 * 7x + x * 7x) = 8(14)
(49x + 7x2) = 8(14)

Multiply 8 * 14
49x + 7x2 = 112

Solving
49x + 7x2 = 112

Solving for variable 'x'.

Reorder the terms:
-112 + 49x + 7x2 = 112 + -112

Combine like terms: 112 + -112 = 0
-112 + 49x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-16 + 7x + x2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-16 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + 7x + x2 = 0

Solving
-16 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 7x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 7x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 7x + x2 = 0 + 16
7x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
7x + x2 = 16

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 16 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 16 + 12.25

Combine like terms: 16 + 12.25 = 28.25
12.25 + 7x + x2 = 28.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(x + 3.5) equal to 5.315072906 and -5.315072906.


Subproblem 1
x + 3.5 = 5.315072906

Simplifying
x + 3.5 = 5.315072906

Reorder the terms:
3.5 + x = 5.315072906

Solving
3.5 + x = 5.315072906

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 5.315072906 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 5.315072906 + -3.5
x = 5.315072906 + -3.5

Combine like terms: 5.315072906 + -3.5 = 1.815072906
x = 1.815072906

Simplifying
x = 1.815072906


Subproblem 2
x + 3.5 = -5.315072906

Simplifying
x + 3.5 = -5.315072906

Reorder the terms:
3.5 + x = -5.315072906

Solving
3.5 + x = -5.315072906

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -5.315072906 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -5.315072906 + -3.5
x = -5.315072906 + -3.5

Combine like terms: -5.315072906 + -3.5 = -8.815072906
x = -8.815072906

Simplifying
x = -8.815072906


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.815072906, -8.815072906}
Solution
x = {1.815072906, -8.815072906}

See similar equations:

| (3r^2+3r-8)(5-2r)= | | 8x+28=84 | | g=y+c-x | | 186=48-v | | 2(x+9)=2x-3 | | (x+10)(3x^2+5x-2)= | | 19-47=3(x-1)-7 | | 166-4x=22 | | 57+w=91 | | 0=-0.03x^2+3.5x-99 | | (y-9)(y/2)=180 | | log(x-1)-log(x-2)=log(5) | | -2+4c=4 | | 7x^3-3x^2-168x=0 | | 64=3y+10 | | (y+5)(x-3)=7 | | M-15=-8 | | 5v-2v=27 | | 3+3(2-3)=4 | | 50-2m^2=0 | | 2-5(2+3)=-3 | | 3+4=6z-9z+2 | | 3*v-12=15 | | sinx-12cosx=6 | | 9b-95=8b-75 | | 0.1z-0.03=-0.07z | | 100=-5(x-1)+4(x-6) | | 6t+12=9t | | 2.4(21/60) | | 2q-11=q+11 | | (y-7)(x-5)=7 | | 43+43+x+94=180 |

Equations solver categories