-x(x+5)=-18

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Solution for -x(x+5)=-18 equation:


Simplifying
-1x(x + 5) = -18

Reorder the terms:
-1x(5 + x) = -18
(5 * -1x + x * -1x) = -18
(-5x + -1x2) = -18

Solving
-5x + -1x2 = -18

Solving for variable 'x'.

Reorder the terms:
18 + -5x + -1x2 = -18 + 18

Combine like terms: -18 + 18 = 0
18 + -5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-18 + 5x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 5x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 5x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 5x + x2 = 0 + 18
5x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
5x + x2 = 18

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 = 18 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 18 + 6.25

Combine like terms: 18 + 6.25 = 24.25
6.25 + 5x + x2 = 24.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.924428901 and -4.924428901.

Subproblem 1

x + 2.5 = 4.924428901 Simplifying x + 2.5 = 4.924428901 Reorder the terms: 2.5 + x = 4.924428901 Solving 2.5 + x = 4.924428901 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 = 4.924428901 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.924428901 + -2.5 x = 4.924428901 + -2.5 Combine like terms: 4.924428901 + -2.5 = 2.424428901 x = 2.424428901 Simplifying x = 2.424428901

Subproblem 2

x + 2.5 = -4.924428901 Simplifying x + 2.5 = -4.924428901 Reorder the terms: 2.5 + x = -4.924428901 Solving 2.5 + x = -4.924428901 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 = -4.924428901 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.924428901 + -2.5 x = -4.924428901 + -2.5 Combine like terms: -4.924428901 + -2.5 = -7.424428901 x = -7.424428901 Simplifying x = -7.424428901

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.424428901, -7.424428901}

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