x(x+5)=210

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Solution for x(x+5)=210 equation:


Simplifying
x(x + 5) = 210

Reorder the terms:
x(5 + x) = 210
(5 * x + x * x) = 210
(5x + x2) = 210

Solving
5x + x2 = 210

Solving for variable 'x'.

Reorder the terms:
-210 + 5x + x2 = 210 + -210

Combine like terms: 210 + -210 = 0
-210 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '210' to each side of the equation.
-210 + 5x + 210 + x2 = 0 + 210

Reorder the terms:
-210 + 210 + 5x + x2 = 0 + 210

Combine like terms: -210 + 210 = 0
0 + 5x + x2 = 0 + 210
5x + x2 = 0 + 210

Combine like terms: 0 + 210 = 210
5x + x2 = 210

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 = 210 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 210 + 6.25

Combine like terms: 210 + 6.25 = 216.25
6.25 + 5x + x2 = 216.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 216.25

Calculate the square root of the right side: 14.70544117

Break this problem into two subproblems by setting 
(x + 2.5) equal to 14.70544117 and -14.70544117.

Subproblem 1

x + 2.5 = 14.70544117 Simplifying x + 2.5 = 14.70544117 Reorder the terms: 2.5 + x = 14.70544117 Solving 2.5 + x = 14.70544117 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 = 14.70544117 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 14.70544117 + -2.5 x = 14.70544117 + -2.5 Combine like terms: 14.70544117 + -2.5 = 12.20544117 x = 12.20544117 Simplifying x = 12.20544117

Subproblem 2

x + 2.5 = -14.70544117 Simplifying x + 2.5 = -14.70544117 Reorder the terms: 2.5 + x = -14.70544117 Solving 2.5 + x = -14.70544117 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 = -14.70544117 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -14.70544117 + -2.5 x = -14.70544117 + -2.5 Combine like terms: -14.70544117 + -2.5 = -17.20544117 x = -17.20544117 Simplifying x = -17.20544117

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.20544117, -17.20544117}

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