2(x-5)(x-5)-1=15

Simple and best practice solution for 2(x-5)(x-5)-1=15 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 2(x-5)(x-5)-1=15 equation: 


Simplifying
2(x + -5)(x + -5) + -1 = 15

Reorder the terms:
2(-5 + x)(x + -5) + -1 = 15

Reorder the terms:
2(-5 + x)(-5 + x) + -1 = 15

Multiply (-5 + x) * (-5 + x)
2(-5(-5 + x) + x(-5 + x)) + -1 = 15
2((-5 * -5 + x * -5) + x(-5 + x)) + -1 = 15
2((25 + -5x) + x(-5 + x)) + -1 = 15
2(25 + -5x + (-5 * x + x * x)) + -1 = 15
2(25 + -5x + (-5x + x2)) + -1 = 15

Combine like terms: -5x + -5x = -10x
2(25 + -10x + x2) + -1 = 15
(25 * 2 + -10x * 2 + x2 * 2) + -1 = 15
(50 + -20x + 2x2) + -1 = 15

Reorder the terms:
50 + -1 + -20x + 2x2 = 15

Combine like terms: 50 + -1 = 49
49 + -20x + 2x2 = 15

Solving
49 + -20x + 2x2 = 15

Solving for variable 'x'.

Reorder the terms:
49 + -15 + -20x + 2x2 = 15 + -15

Combine like terms: 49 + -15 = 34
34 + -20x + 2x2 = 15 + -15

Combine like terms: 15 + -15 = 0
34 + -20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + -10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(17 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
17 + -10x + x2 = 0

Solving
17 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -10x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + -10x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -10x + x2 = 0 + -17
-10x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
-10x + x2 = -17

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -17 + 25

Reorder the terms:
25 + -10x + x2 = -17 + 25

Combine like terms: -17 + 25 = 8
25 + -10x + x2 = 8

Factor a perfect square on the left side:
(x + -5)(x + -5) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -5) equal to 2.828427125 and -2.828427125.


Subproblem 1
x + -5 = 2.828427125

Simplifying
x + -5 = 2.828427125

Reorder the terms:
-5 + x = 2.828427125

Solving
-5 + x = 2.828427125

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 2.828427125 + 5

Combine like terms: -5 + 5 = 0
0 + x = 2.828427125 + 5
x = 2.828427125 + 5

Combine like terms: 2.828427125 + 5 = 7.828427125
x = 7.828427125

Simplifying
x = 7.828427125


Subproblem 2
x + -5 = -2.828427125

Simplifying
x + -5 = -2.828427125

Reorder the terms:
-5 + x = -2.828427125

Solving
-5 + x = -2.828427125

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -2.828427125 + 5

Combine like terms: -5 + 5 = 0
0 + x = -2.828427125 + 5
x = -2.828427125 + 5

Combine like terms: -2.828427125 + 5 = 2.171572875
x = 2.171572875

Simplifying
x = 2.171572875


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.828427125, 2.171572875}
Solution
x = {7.828427125, 2.171572875}

See similar equations:

| x+3=14.1 | | 25m^2-36=0 | | 4x+4=68 | | 7s+2=4n+17 | | 3(10.75)+6(11.75)-7(8.25)=12 | | 3x=14.1 | | W=235-2.5 | | X+10+2x-5+2x+20=180 | | 58y=19(3y+1) | | 3p-10=4 | | 4t+4t=16 | | x-3=14.1 | | n(n-4)+n(n+8)=n(n-13)+n(n+1)16 | | -17p+7p+8p=-20 | | X+10+2x-5+2x+20= | | X^2-21x-20=0 | | 23.6*23.6+15*15=x*x | | 3log(8x)-2=7 | | 3t+-4=-13 | | -1x-3y=24 | | 2z+45=21 | | 4x+6=8x+18 | | 4x-15-x=6 | | 5x^2+12=22 | | 12.5+.4e=14.75+.25e | | 4x+6=10x+18 | | -2x+(-5)=2+(-x) | | 3-3=17x+8x | | 12x-5=2x-4 | | zw=12x-xy | | 10k^2-41k+21=0 | | 9w+8= |

Equations solver categories