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

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


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

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

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

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

Combine like terms: -1x + 5x = 4x
(-5 + 4x + x2) = 5

Solving
-5 + 4x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + -5 + 4x + x2 = 5 + -5

Combine like terms: -5 + -5 = -10
-10 + 4x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-10 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 4x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 4x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 4x + x2 = 0 + 10
4x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
4x + x2 = 10

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 10 + 4

Reorder the terms:
4 + 4x + x2 = 10 + 4

Combine like terms: 10 + 4 = 14
4 + 4x + x2 = 14

Factor a perfect square on the left side:
(x + 2)(x + 2) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + 2) equal to 3.741657387 and -3.741657387.

Subproblem 1

x + 2 = 3.741657387 Simplifying x + 2 = 3.741657387 Reorder the terms: 2 + x = 3.741657387 Solving 2 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.741657387 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.741657387 + -2 x = 3.741657387 + -2 Combine like terms: 3.741657387 + -2 = 1.741657387 x = 1.741657387 Simplifying x = 1.741657387

Subproblem 2

x + 2 = -3.741657387 Simplifying x + 2 = -3.741657387 Reorder the terms: 2 + x = -3.741657387 Solving 2 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.741657387 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.741657387 + -2 x = -3.741657387 + -2 Combine like terms: -3.741657387 + -2 = -5.741657387 x = -5.741657387 Simplifying x = -5.741657387

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.741657387, -5.741657387}

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