x(5+2x)=532

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Solution for x(5+2x)=532 equation:


Simplifying
x(5 + 2x) = 532
(5 * x + 2x * x) = 532
(5x + 2x2) = 532

Solving
5x + 2x2 = 532

Solving for variable 'x'.

Reorder the terms:
-532 + 5x + 2x2 = 532 + -532

Combine like terms: 532 + -532 = 0
-532 + 5x + 2x2 = 0

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

Divide each side by '2'.
-266 + 2.5x + x2 = 0

Move the constant term to the right:

Add '266' to each side of the equation.
-266 + 2.5x + 266 + x2 = 0 + 266

Reorder the terms:
-266 + 266 + 2.5x + x2 = 0 + 266

Combine like terms: -266 + 266 = 0
0 + 2.5x + x2 = 0 + 266
2.5x + x2 = 0 + 266

Combine like terms: 0 + 266 = 266
2.5x + x2 = 266

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 266 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 266 + 1.5625

Combine like terms: 266 + 1.5625 = 267.5625
1.5625 + 2.5x + x2 = 267.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 267.5625

Calculate the square root of the right side: 16.357337803

Break this problem into two subproblems by setting 
(x + 1.25) equal to 16.357337803 and -16.357337803.

Subproblem 1

x + 1.25 = 16.357337803 Simplifying x + 1.25 = 16.357337803 Reorder the terms: 1.25 + x = 16.357337803 Solving 1.25 + x = 16.357337803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 16.357337803 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 16.357337803 + -1.25 x = 16.357337803 + -1.25 Combine like terms: 16.357337803 + -1.25 = 15.107337803 x = 15.107337803 Simplifying x = 15.107337803

Subproblem 2

x + 1.25 = -16.357337803 Simplifying x + 1.25 = -16.357337803 Reorder the terms: 1.25 + x = -16.357337803 Solving 1.25 + x = -16.357337803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -16.357337803 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -16.357337803 + -1.25 x = -16.357337803 + -1.25 Combine like terms: -16.357337803 + -1.25 = -17.607337803 x = -17.607337803 Simplifying x = -17.607337803

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.107337803, -17.607337803}

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