4(x-7)(x-7)=52

Simple and best practice solution for 4(x-7)(x-7)=52 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 4(x-7)(x-7)=52 equation: 


Simplifying
4(x + -7)(x + -7) = 52

Reorder the terms:
4(-7 + x)(x + -7) = 52

Reorder the terms:
4(-7 + x)(-7 + x) = 52

Multiply (-7 + x) * (-7 + x)
4(-7(-7 + x) + x(-7 + x)) = 52
4((-7 * -7 + x * -7) + x(-7 + x)) = 52
4((49 + -7x) + x(-7 + x)) = 52
4(49 + -7x + (-7 * x + x * x)) = 52
4(49 + -7x + (-7x + x2)) = 52

Combine like terms: -7x + -7x = -14x
4(49 + -14x + x2) = 52
(49 * 4 + -14x * 4 + x2 * 4) = 52
(196 + -56x + 4x2) = 52

Solving
196 + -56x + 4x2 = 52

Solving for variable 'x'.

Reorder the terms:
196 + -52 + -56x + 4x2 = 52 + -52

Combine like terms: 196 + -52 = 144
144 + -56x + 4x2 = 52 + -52

Combine like terms: 52 + -52 = 0
144 + -56x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(36 + -14x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(36 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
36 + -14x + x2 = 0

Solving
36 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -14x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + -14x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -14x + x2 = 0 + -36
-14x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
-14x + x2 = -36

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -36 + 49

Reorder the terms:
49 + -14x + x2 = -36 + 49

Combine like terms: -36 + 49 = 13
49 + -14x + x2 = 13

Factor a perfect square on the left side:
(x + -7)(x + -7) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -7) equal to 3.605551275 and -3.605551275.


Subproblem 1
x + -7 = 3.605551275

Simplifying
x + -7 = 3.605551275

Reorder the terms:
-7 + x = 3.605551275

Solving
-7 + x = 3.605551275

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 3.605551275 + 7

Combine like terms: -7 + 7 = 0
0 + x = 3.605551275 + 7
x = 3.605551275 + 7

Combine like terms: 3.605551275 + 7 = 10.605551275
x = 10.605551275

Simplifying
x = 10.605551275


Subproblem 2
x + -7 = -3.605551275

Simplifying
x + -7 = -3.605551275

Reorder the terms:
-7 + x = -3.605551275

Solving
-7 + x = -3.605551275

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -3.605551275 + 7

Combine like terms: -7 + 7 = 0
0 + x = -3.605551275 + 7
x = -3.605551275 + 7

Combine like terms: -3.605551275 + 7 = 3.394448725
x = 3.394448725

Simplifying
x = 3.394448725


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.605551275, 3.394448725}
Solution
x = {10.605551275, 3.394448725}

See similar equations:

| 5y-2y=42 | | 2(2x-3)=19+5x | | 4(x+7)=-32+6x | | 122-4x=14x+18 | | y/2-7=5 | | 2(4x+15)=7(x+2) | | 7+2.5y=0.6y-4 | | 56-12y=80-8y | | (35)-6=(15x-10)-(63x+56) | | 0=(6x^2)-6x-72 | | 6=5+.5a | | 4(y-9)-10Y=0 | | -52=-4m | | 10x^2+21x-10=o | | -3y-8=7y+22 | | 9-7x=33-28x | | 8[4-3(a-3)]=8(3-4a) | | 6(x-2)=4+6x | | 6-(n+3)=3(n-2) | | 4=5+.5a | | -3r+4=2r+4 | | 135+3k=180 | | f+3.14=12.314 | | -122-4x=14x+18 | | 5[4-2(a-2)]=5(2-4a) | | 4x-6y=-2 | | -35=-8x+5 | | 3x+19=34 | | (16w-24)+(21w+21)=9(12) | | P(x)=x^3-6x^2-17x+8 | | 8x^2-36x=0 | | 4t+(-4t)=-2 |

Equations solver categories