5x(x+7)=25

Simple and best practice solution for 5x(x+7)=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 5x(x+7)=25 equation: 


Simplifying
5x(x + 7) = 25

Reorder the terms:
5x(7 + x) = 25
(7 * 5x + x * 5x) = 25
(35x + 5x2) = 25

Solving
35x + 5x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + 35x + 5x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 35x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + 7x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-5 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-5 + 7x + x2 = 0

Solving
-5 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 7x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 7x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 7x + x2 = 0 + 5
7x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
7x + x2 = 5

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 = 5 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 5 + 12.25

Combine like terms: 5 + 12.25 = 17.25
12.25 + 7x + x2 = 17.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.153311931 and -4.153311931.


Subproblem 1
x + 3.5 = 4.153311931

Simplifying
x + 3.5 = 4.153311931

Reorder the terms:
3.5 + x = 4.153311931

Solving
3.5 + x = 4.153311931

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 = 4.153311931 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.153311931 + -3.5
x = 4.153311931 + -3.5

Combine like terms: 4.153311931 + -3.5 = 0.653311931
x = 0.653311931

Simplifying
x = 0.653311931


Subproblem 2
x + 3.5 = -4.153311931

Simplifying
x + 3.5 = -4.153311931

Reorder the terms:
3.5 + x = -4.153311931

Solving
3.5 + x = -4.153311931

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 = -4.153311931 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.153311931 + -3.5
x = -4.153311931 + -3.5

Combine like terms: -4.153311931 + -3.5 = -7.653311931
x = -7.653311931

Simplifying
x = -7.653311931


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.653311931, -7.653311931}
Solution
x = {0.653311931, -7.653311931}

See similar equations:

| 240=16n | | c=8x+5y | | xy+2x+3y=8 | | cx-x=v | | (4x+8)+(-2x+1)= | | 6qr+7rs-2st=-9x | | 2x^2+xy-15y^2=51 | | 8x^2-32x^3=0 | | -8.6(-84u-68)=-17.2(8u-93) | | -2z-xy=x+7x | | -17k=-34 | | 2x+11=3.5 | | 9(3d-7)= | | 108=-12x | | 3(b+6)=8(14b-(12b-5)) | | (4x+8)-(2x-1)= | | 3a=-84 | | 8(L-6)= | | ax+yx=n | | 4(l+7)= | | 3y^1=x^2 | | 4y+9x=5 | | x^2-y^2=24 | | 3x+28=37 | | x-29=-32 | | 2(3x+5)=-20 | | 3x+18=3(5x-2) | | 4p-2=16 | | 5(y-7)=50 | | (x^2+x-6)(-2x^2+12x+80)=o | | 3(a+2)=36 | | -29x=319 |

Equations solver categories