x^2+3x=7x+34

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Solution for x^2+3x=7x+34 equation:


Simplifying
x2 + 3x = 7x + 34

Reorder the terms:
3x + x2 = 7x + 34

Reorder the terms:
3x + x2 = 34 + 7x

Solving
3x + x2 = 34 + 7x

Solving for variable 'x'.

Reorder the terms:
-34 + 3x + -7x + x2 = 34 + 7x + -34 + -7x

Combine like terms: 3x + -7x = -4x
-34 + -4x + x2 = 34 + 7x + -34 + -7x

Reorder the terms:
-34 + -4x + x2 = 34 + -34 + 7x + -7x

Combine like terms: 34 + -34 = 0
-34 + -4x + x2 = 0 + 7x + -7x
-34 + -4x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-34 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + -4x + 34 + x2 = 0 + 34

Reorder the terms:
-34 + 34 + -4x + x2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -4x + x2 = 0 + 34
-4x + x2 = 0 + 34

Combine like terms: 0 + 34 = 34
-4x + x2 = 34

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 34 + 4

Reorder the terms:
4 + -4x + x2 = 34 + 4

Combine like terms: 34 + 4 = 38
4 + -4x + x2 = 38

Factor a perfect square on the left side:
(x + -2)(x + -2) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(x + -2) equal to 6.164414003 and -6.164414003.


Subproblem 1
x + -2 = 6.164414003

Simplifying
x + -2 = 6.164414003

Reorder the terms:
-2 + x = 6.164414003

Solving
-2 + x = 6.164414003

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = 6.164414003 + 2

Combine like terms: -2 + 2 = 0
0 + x = 6.164414003 + 2
x = 6.164414003 + 2

Combine like terms: 6.164414003 + 2 = 8.164414003
x = 8.164414003

Simplifying
x = 8.164414003


Subproblem 2
x + -2 = -6.164414003

Simplifying
x + -2 = -6.164414003

Reorder the terms:
-2 + x = -6.164414003

Solving
-2 + x = -6.164414003

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = -6.164414003 + 2

Combine like terms: -2 + 2 = 0
0 + x = -6.164414003 + 2
x = -6.164414003 + 2

Combine like terms: -6.164414003 + 2 = -4.164414003
x = -4.164414003

Simplifying
x = -4.164414003


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.164414003, -4.164414003}

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