(x-5)(x-5)=75

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Solution for (x-5)(x-5)=75 equation:


Simplifying
(x + -5)(x + -5) = 75

Reorder the terms:
(-5 + x)(x + -5) = 75

Reorder the terms:
(-5 + x)(-5 + x) = 75

Multiply (-5 + x) * (-5 + x)
(-5(-5 + x) + x(-5 + x)) = 75
((-5 * -5 + x * -5) + x(-5 + x)) = 75
((25 + -5x) + x(-5 + x)) = 75
(25 + -5x + (-5 * x + x * x)) = 75
(25 + -5x + (-5x + x2)) = 75

Combine like terms: -5x + -5x = -10x
(25 + -10x + x2) = 75

Solving
25 + -10x + x2 = 75

Solving for variable 'x'.

Reorder the terms:
25 + -75 + -10x + x2 = 75 + -75

Combine like terms: 25 + -75 = -50
-50 + -10x + x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-50 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -10x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + -10x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -10x + x2 = 0 + 50
-10x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
-10x + x2 = 50

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 = 50 + 25

Reorder the terms:
25 + -10x + x2 = 50 + 25

Combine like terms: 50 + 25 = 75
25 + -10x + x2 = 75

Factor a perfect square on the left side:
(x + -5)(x + -5) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + -5) equal to 8.660254038 and -8.660254038.

Subproblem 1

x + -5 = 8.660254038 Simplifying x + -5 = 8.660254038 Reorder the terms: -5 + x = 8.660254038 Solving -5 + x = 8.660254038 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 = 8.660254038 + 5 Combine like terms: -5 + 5 = 0 0 + x = 8.660254038 + 5 x = 8.660254038 + 5 Combine like terms: 8.660254038 + 5 = 13.660254038 x = 13.660254038 Simplifying x = 13.660254038

Subproblem 2

x + -5 = -8.660254038 Simplifying x + -5 = -8.660254038 Reorder the terms: -5 + x = -8.660254038 Solving -5 + x = -8.660254038 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 = -8.660254038 + 5 Combine like terms: -5 + 5 = 0 0 + x = -8.660254038 + 5 x = -8.660254038 + 5 Combine like terms: -8.660254038 + 5 = -3.660254038 x = -3.660254038 Simplifying x = -3.660254038

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.660254038, -3.660254038}

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