x(x+5)-4=0

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Solution for x(x+5)-4=0 equation:


Simplifying
x(x + 5) + -4 = 0

Reorder the terms:
x(5 + x) + -4 = 0
(5 * x + x * x) + -4 = 0
(5x + x2) + -4 = 0

Reorder the terms:
-4 + 5x + x2 = 0

Solving
-4 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 5x + x2 = 0 + 4

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

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

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 4 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 4 + 6.25

Combine like terms: 4 + 6.25 = 10.25
6.25 + 5x + x2 = 10.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

x + 2.5 = 3.201562119 Simplifying x + 2.5 = 3.201562119 Reorder the terms: 2.5 + x = 3.201562119 Solving 2.5 + x = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.201562119 + -2.5 x = 3.201562119 + -2.5 Combine like terms: 3.201562119 + -2.5 = 0.701562119 x = 0.701562119 Simplifying x = 0.701562119

Subproblem 2

x + 2.5 = -3.201562119 Simplifying x + 2.5 = -3.201562119 Reorder the terms: 2.5 + x = -3.201562119 Solving 2.5 + x = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.201562119 + -2.5 x = -3.201562119 + -2.5 Combine like terms: -3.201562119 + -2.5 = -5.701562119 x = -5.701562119 Simplifying x = -5.701562119

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.701562119, -5.701562119}

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