x(x+5)=287

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Solution for x(x+5)=287 equation:


Simplifying
x(x + 5) = 287

Reorder the terms:
x(5 + x) = 287
(5 * x + x * x) = 287
(5x + x2) = 287

Solving
5x + x2 = 287

Solving for variable 'x'.

Reorder the terms:
-287 + 5x + x2 = 287 + -287

Combine like terms: 287 + -287 = 0
-287 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '287' to each side of the equation.
-287 + 5x + 287 + x2 = 0 + 287

Reorder the terms:
-287 + 287 + 5x + x2 = 0 + 287

Combine like terms: -287 + 287 = 0
0 + 5x + x2 = 0 + 287
5x + x2 = 0 + 287

Combine like terms: 0 + 287 = 287
5x + x2 = 287

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 = 287 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 287 + 6.25

Combine like terms: 287 + 6.25 = 293.25
6.25 + 5x + x2 = 293.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 293.25

Calculate the square root of the right side: 17.12454379

Break this problem into two subproblems by setting 
(x + 2.5) equal to 17.12454379 and -17.12454379.

Subproblem 1

x + 2.5 = 17.12454379 Simplifying x + 2.5 = 17.12454379 Reorder the terms: 2.5 + x = 17.12454379 Solving 2.5 + x = 17.12454379 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 = 17.12454379 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 17.12454379 + -2.5 x = 17.12454379 + -2.5 Combine like terms: 17.12454379 + -2.5 = 14.62454379 x = 14.62454379 Simplifying x = 14.62454379

Subproblem 2

x + 2.5 = -17.12454379 Simplifying x + 2.5 = -17.12454379 Reorder the terms: 2.5 + x = -17.12454379 Solving 2.5 + x = -17.12454379 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 = -17.12454379 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -17.12454379 + -2.5 x = -17.12454379 + -2.5 Combine like terms: -17.12454379 + -2.5 = -19.62454379 x = -19.62454379 Simplifying x = -19.62454379

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.62454379, -19.62454379}

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