x(x+2)=625

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Solution for x(x+2)=625 equation:


Simplifying
x(x + 2) = 625

Reorder the terms:
x(2 + x) = 625
(2 * x + x * x) = 625
(2x + x2) = 625

Solving
2x + x2 = 625

Solving for variable 'x'.

Reorder the terms:
-625 + 2x + x2 = 625 + -625

Combine like terms: 625 + -625 = 0
-625 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '625' to each side of the equation.
-625 + 2x + 625 + x2 = 0 + 625

Reorder the terms:
-625 + 625 + 2x + x2 = 0 + 625

Combine like terms: -625 + 625 = 0
0 + 2x + x2 = 0 + 625
2x + x2 = 0 + 625

Combine like terms: 0 + 625 = 625
2x + x2 = 625

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 625 + 1

Reorder the terms:
1 + 2x + x2 = 625 + 1

Combine like terms: 625 + 1 = 626
1 + 2x + x2 = 626

Factor a perfect square on the left side:
(x + 1)(x + 1) = 626

Calculate the square root of the right side: 25.019992006

Break this problem into two subproblems by setting 
(x + 1) equal to 25.019992006 and -25.019992006.

Subproblem 1

x + 1 = 25.019992006 Simplifying x + 1 = 25.019992006 Reorder the terms: 1 + x = 25.019992006 Solving 1 + x = 25.019992006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 25.019992006 + -1 Combine like terms: 1 + -1 = 0 0 + x = 25.019992006 + -1 x = 25.019992006 + -1 Combine like terms: 25.019992006 + -1 = 24.019992006 x = 24.019992006 Simplifying x = 24.019992006

Subproblem 2

x + 1 = -25.019992006 Simplifying x + 1 = -25.019992006 Reorder the terms: 1 + x = -25.019992006 Solving 1 + x = -25.019992006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -25.019992006 + -1 Combine like terms: 1 + -1 = 0 0 + x = -25.019992006 + -1 x = -25.019992006 + -1 Combine like terms: -25.019992006 + -1 = -26.019992006 x = -26.019992006 Simplifying x = -26.019992006

Solution

The solution to the problem is based on the solutions from the subproblems. x = {24.019992006, -26.019992006}

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