x(x+3)=34

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Solution for x(x+3)=34 equation: 


Simplifying
x(x + 3) = 34

Reorder the terms:
x(3 + x) = 34
(3 * x + x * x) = 34
(3x + x2) = 34

Solving
3x + x2 = 34

Solving for variable 'x'.

Reorder the terms:
-34 + 3x + x2 = 34 + -34

Combine like terms: 34 + -34 = 0
-34 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + 3x + 34 + x2 = 0 + 34

Reorder the terms:
-34 + 34 + 3x + x2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + 3x + x2 = 0 + 34
3x + x2 = 0 + 34

Combine like terms: 0 + 34 = 34
3x + x2 = 34

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 = 34 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 34 + 2.25

Combine like terms: 34 + 2.25 = 36.25
2.25 + 3x + x2 = 36.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(x + 1.5) equal to 6.020797289 and -6.020797289.


Subproblem 1
x + 1.5 = 6.020797289

Simplifying
x + 1.5 = 6.020797289

Reorder the terms:
1.5 + x = 6.020797289

Solving
1.5 + x = 6.020797289

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 = 6.020797289 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 6.020797289 + -1.5
x = 6.020797289 + -1.5

Combine like terms: 6.020797289 + -1.5 = 4.520797289
x = 4.520797289

Simplifying
x = 4.520797289


Subproblem 2
x + 1.5 = -6.020797289

Simplifying
x + 1.5 = -6.020797289

Reorder the terms:
1.5 + x = -6.020797289

Solving
1.5 + x = -6.020797289

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 = -6.020797289 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -6.020797289 + -1.5
x = -6.020797289 + -1.5

Combine like terms: -6.020797289 + -1.5 = -7.520797289
x = -7.520797289

Simplifying
x = -7.520797289


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.520797289, -7.520797289}

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