(x-5)(x-1)=280

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Solution for (x-5)(x-1)=280 equation:


Simplifying
(x + -5)(x + -1) = 280

Reorder the terms:
(-5 + x)(x + -1) = 280

Reorder the terms:
(-5 + x)(-1 + x) = 280

Multiply (-5 + x) * (-1 + x)
(-5(-1 + x) + x(-1 + x)) = 280
((-1 * -5 + x * -5) + x(-1 + x)) = 280
((5 + -5x) + x(-1 + x)) = 280
(5 + -5x + (-1 * x + x * x)) = 280
(5 + -5x + (-1x + x2)) = 280

Combine like terms: -5x + -1x = -6x
(5 + -6x + x2) = 280

Solving
5 + -6x + x2 = 280

Solving for variable 'x'.

Reorder the terms:
5 + -280 + -6x + x2 = 280 + -280

Combine like terms: 5 + -280 = -275
-275 + -6x + x2 = 280 + -280

Combine like terms: 280 + -280 = 0
-275 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '275' to each side of the equation.
-275 + -6x + 275 + x2 = 0 + 275

Reorder the terms:
-275 + 275 + -6x + x2 = 0 + 275

Combine like terms: -275 + 275 = 0
0 + -6x + x2 = 0 + 275
-6x + x2 = 0 + 275

Combine like terms: 0 + 275 = 275
-6x + x2 = 275

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 275 + 9

Reorder the terms:
9 + -6x + x2 = 275 + 9

Combine like terms: 275 + 9 = 284
9 + -6x + x2 = 284

Factor a perfect square on the left side:
(x + -3)(x + -3) = 284

Calculate the square root of the right side: 16.852299546

Break this problem into two subproblems by setting 
(x + -3) equal to 16.852299546 and -16.852299546.

Subproblem 1

x + -3 = 16.852299546 Simplifying x + -3 = 16.852299546 Reorder the terms: -3 + x = 16.852299546 Solving -3 + x = 16.852299546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 16.852299546 + 3 Combine like terms: -3 + 3 = 0 0 + x = 16.852299546 + 3 x = 16.852299546 + 3 Combine like terms: 16.852299546 + 3 = 19.852299546 x = 19.852299546 Simplifying x = 19.852299546

Subproblem 2

x + -3 = -16.852299546 Simplifying x + -3 = -16.852299546 Reorder the terms: -3 + x = -16.852299546 Solving -3 + x = -16.852299546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -16.852299546 + 3 Combine like terms: -3 + 3 = 0 0 + x = -16.852299546 + 3 x = -16.852299546 + 3 Combine like terms: -16.852299546 + 3 = -13.852299546 x = -13.852299546 Simplifying x = -13.852299546

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.852299546, -13.852299546}

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