15(2x+7)(2x+7)=75

Simple and best practice solution for 15(2x+7)(2x+7)=75 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 15(2x+7)(2x+7)=75 equation: 


Simplifying
15(2x + 7)(2x + 7) = 75

Reorder the terms:
15(7 + 2x)(2x + 7) = 75

Reorder the terms:
15(7 + 2x)(7 + 2x) = 75

Multiply (7 + 2x) * (7 + 2x)
15(7(7 + 2x) + 2x * (7 + 2x)) = 75
15((7 * 7 + 2x * 7) + 2x * (7 + 2x)) = 75
15((49 + 14x) + 2x * (7 + 2x)) = 75
15(49 + 14x + (7 * 2x + 2x * 2x)) = 75
15(49 + 14x + (14x + 4x2)) = 75

Combine like terms: 14x + 14x = 28x
15(49 + 28x + 4x2) = 75
(49 * 15 + 28x * 15 + 4x2 * 15) = 75
(735 + 420x + 60x2) = 75

Solving
735 + 420x + 60x2 = 75

Solving for variable 'x'.

Reorder the terms:
735 + -75 + 420x + 60x2 = 75 + -75

Combine like terms: 735 + -75 = 660
660 + 420x + 60x2 = 75 + -75

Combine like terms: 75 + -75 = 0
660 + 420x + 60x2 = 0

Factor out the Greatest Common Factor (GCF), '60'.
60(11 + 7x + x2) = 0

Ignore the factor 60.

Subproblem 1
Set the factor '(11 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
11 + 7x + x2 = 0

Solving
11 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 7x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + 7x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 7x + x2 = 0 + -11
7x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
7x + x2 = -11

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 = -11 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -11 + 12.25

Combine like terms: -11 + 12.25 = 1.25
12.25 + 7x + x2 = 1.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + 3.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
x + 3.5 = 1.118033989

Simplifying
x + 3.5 = 1.118033989

Reorder the terms:
3.5 + x = 1.118033989

Solving
3.5 + x = 1.118033989

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 = 1.118033989 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 1.118033989 + -3.5
x = 1.118033989 + -3.5

Combine like terms: 1.118033989 + -3.5 = -2.381966011
x = -2.381966011

Simplifying
x = -2.381966011


Subproblem 2
x + 3.5 = -1.118033989

Simplifying
x + 3.5 = -1.118033989

Reorder the terms:
3.5 + x = -1.118033989

Solving
3.5 + x = -1.118033989

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 = -1.118033989 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -1.118033989 + -3.5
x = -1.118033989 + -3.5

Combine like terms: -1.118033989 + -3.5 = -4.618033989
x = -4.618033989

Simplifying
x = -4.618033989


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.381966011, -4.618033989}
Solution
x = {-2.381966011, -4.618033989}

See similar equations:

| -4x-8=-4/4 | | 5x+3=6x-19 | | 7+8u+3-16u=36 | | 3(2s+6)=6(s+2)-24s | | 4-6+2-6r+7r= | | 1.6=3.2x | | (x+2)+90=128 | | 3x+62=110 | | j/19-2=(-5) | | 6(8+c)= | | -1(2a+3a-7)= | | 5r-7r+2+6r= | | V=kWh | | 4=-(x+-7)+3 | | -3(b-(-7))= | | 3x+1=130 | | 4(a-4)-2=34 | | 42=16-2/3a | | -5p-5p+-7+-2+-2p= | | (x+20)+x=80 | | 9s+77=-1-4s | | 4=(x+-7)+3 | | 7(c-4)=(4-c)(3) | | 2p^2-21p-2=0 | | -40=b-5 | | 2x-5-6x=3x-3 | | 6x+15-8x=20-15x+13x-5 | | 3=-(x+4)-11 | | 0=30p | | 3x+1(2x)=126 | | 6(2-4n)=5n-162 | | -2(2x+1)-2=2(12-x) |

Equations solver categories