x(x+3)=207

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Solution for x(x+3)=207 equation:


Simplifying
x(x + 3) = 207

Reorder the terms:
x(3 + x) = 207
(3 * x + x * x) = 207
(3x + x2) = 207

Solving
3x + x2 = 207

Solving for variable 'x'.

Reorder the terms:
-207 + 3x + x2 = 207 + -207

Combine like terms: 207 + -207 = 0
-207 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '207' to each side of the equation.
-207 + 3x + 207 + x2 = 0 + 207

Reorder the terms:
-207 + 207 + 3x + x2 = 0 + 207

Combine like terms: -207 + 207 = 0
0 + 3x + x2 = 0 + 207
3x + x2 = 0 + 207

Combine like terms: 0 + 207 = 207
3x + x2 = 207

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 = 207 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 207 + 2.25

Combine like terms: 207 + 2.25 = 209.25
2.25 + 3x + x2 = 209.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 209.25

Calculate the square root of the right side: 14.465476141

Break this problem into two subproblems by setting 
(x + 1.5) equal to 14.465476141 and -14.465476141.

Subproblem 1

x + 1.5 = 14.465476141 Simplifying x + 1.5 = 14.465476141 Reorder the terms: 1.5 + x = 14.465476141 Solving 1.5 + x = 14.465476141 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 = 14.465476141 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 14.465476141 + -1.5 x = 14.465476141 + -1.5 Combine like terms: 14.465476141 + -1.5 = 12.965476141 x = 12.965476141 Simplifying x = 12.965476141

Subproblem 2

x + 1.5 = -14.465476141 Simplifying x + 1.5 = -14.465476141 Reorder the terms: 1.5 + x = -14.465476141 Solving 1.5 + x = -14.465476141 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 = -14.465476141 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -14.465476141 + -1.5 x = -14.465476141 + -1.5 Combine like terms: -14.465476141 + -1.5 = -15.965476141 x = -15.965476141 Simplifying x = -15.965476141

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.965476141, -15.965476141}

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