4(x^2-10x-7)=0

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Solution for 4(x^2-10x-7)=0 equation: 


Simplifying
4(x2 + -10x + -7) = 0

Reorder the terms:
4(-7 + -10x + x2) = 0
(-7 * 4 + -10x * 4 + x2 * 4) = 0
(-28 + -40x + 4x2) = 0

Solving
-28 + -40x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-7 + -10x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-7 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
-7 + -10x + x2 = 0

Solving
-7 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -10x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -10x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -10x + x2 = 0 + 7
-10x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-10x + x2 = 7

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 = 7 + 25

Reorder the terms:
25 + -10x + x2 = 7 + 25

Combine like terms: 7 + 25 = 32
25 + -10x + x2 = 32

Factor a perfect square on the left side:
(x + -5)(x + -5) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + -5) equal to 5.656854249 and -5.656854249.


Subproblem 1
x + -5 = 5.656854249

Simplifying
x + -5 = 5.656854249

Reorder the terms:
-5 + x = 5.656854249

Solving
-5 + x = 5.656854249

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 = 5.656854249 + 5

Combine like terms: -5 + 5 = 0
0 + x = 5.656854249 + 5
x = 5.656854249 + 5

Combine like terms: 5.656854249 + 5 = 10.656854249
x = 10.656854249

Simplifying
x = 10.656854249


Subproblem 2
x + -5 = -5.656854249

Simplifying
x + -5 = -5.656854249

Reorder the terms:
-5 + x = -5.656854249

Solving
-5 + x = -5.656854249

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 = -5.656854249 + 5

Combine like terms: -5 + 5 = 0
0 + x = -5.656854249 + 5
x = -5.656854249 + 5

Combine like terms: -5.656854249 + 5 = -0.656854249
x = -0.656854249

Simplifying
x = -0.656854249


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.656854249, -0.656854249}
Solution
x = {10.656854249, -0.656854249}

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