5x(x+2)=126

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Solution for 5x(x+2)=126 equation:


Simplifying
5x(x + 2) = 126

Reorder the terms:
5x(2 + x) = 126
(2 * 5x + x * 5x) = 126
(10x + 5x2) = 126

Solving
10x + 5x2 = 126

Solving for variable 'x'.

Reorder the terms:
-126 + 10x + 5x2 = 126 + -126

Combine like terms: 126 + -126 = 0
-126 + 10x + 5x2 = 0

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

Divide each side by '5'.
-25.2 + 2x + x2 = 0

Move the constant term to the right:

Add '25.2' to each side of the equation.
-25.2 + 2x + 25.2 + x2 = 0 + 25.2

Reorder the terms:
-25.2 + 25.2 + 2x + x2 = 0 + 25.2

Combine like terms: -25.2 + 25.2 = 0.0
0.0 + 2x + x2 = 0 + 25.2
2x + x2 = 0 + 25.2

Combine like terms: 0 + 25.2 = 25.2
2x + x2 = 25.2

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 = 25.2 + 1

Reorder the terms:
1 + 2x + x2 = 25.2 + 1

Combine like terms: 25.2 + 1 = 26.2
1 + 2x + x2 = 26.2

Factor a perfect square on the left side:
(x + 1)(x + 1) = 26.2

Calculate the square root of the right side: 5.118593557

Break this problem into two subproblems by setting 
(x + 1) equal to 5.118593557 and -5.118593557.

Subproblem 1

x + 1 = 5.118593557 Simplifying x + 1 = 5.118593557 Reorder the terms: 1 + x = 5.118593557 Solving 1 + x = 5.118593557 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 = 5.118593557 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.118593557 + -1 x = 5.118593557 + -1 Combine like terms: 5.118593557 + -1 = 4.118593557 x = 4.118593557 Simplifying x = 4.118593557

Subproblem 2

x + 1 = -5.118593557 Simplifying x + 1 = -5.118593557 Reorder the terms: 1 + x = -5.118593557 Solving 1 + x = -5.118593557 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 = -5.118593557 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.118593557 + -1 x = -5.118593557 + -1 Combine like terms: -5.118593557 + -1 = -6.118593557 x = -6.118593557 Simplifying x = -6.118593557

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.118593557, -6.118593557}

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