x(x+3)=511

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Solution for x(x+3)=511 equation:


Simplifying
x(x + 3) = 511

Reorder the terms:
x(3 + x) = 511
(3 * x + x * x) = 511
(3x + x2) = 511

Solving
3x + x2 = 511

Solving for variable 'x'.

Reorder the terms:
-511 + 3x + x2 = 511 + -511

Combine like terms: 511 + -511 = 0
-511 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '511' to each side of the equation.
-511 + 3x + 511 + x2 = 0 + 511

Reorder the terms:
-511 + 511 + 3x + x2 = 0 + 511

Combine like terms: -511 + 511 = 0
0 + 3x + x2 = 0 + 511
3x + x2 = 0 + 511

Combine like terms: 0 + 511 = 511
3x + x2 = 511

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 511 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 511 + 2.25

Combine like terms: 511 + 2.25 = 513.25
2.25 + 3x + x2 = 513.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 513.25

Calculate the square root of the right side: 22.655021518

Break this problem into two subproblems by setting 
(x + 1.5) equal to 22.655021518 and -22.655021518.

Subproblem 1

x + 1.5 = 22.655021518 Simplifying x + 1.5 = 22.655021518 Reorder the terms: 1.5 + x = 22.655021518 Solving 1.5 + x = 22.655021518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 22.655021518 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 22.655021518 + -1.5 x = 22.655021518 + -1.5 Combine like terms: 22.655021518 + -1.5 = 21.155021518 x = 21.155021518 Simplifying x = 21.155021518

Subproblem 2

x + 1.5 = -22.655021518 Simplifying x + 1.5 = -22.655021518 Reorder the terms: 1.5 + x = -22.655021518 Solving 1.5 + x = -22.655021518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -22.655021518 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -22.655021518 + -1.5 x = -22.655021518 + -1.5 Combine like terms: -22.655021518 + -1.5 = -24.155021518 x = -24.155021518 Simplifying x = -24.155021518

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21.155021518, -24.155021518}

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