x^2+4x+4=375

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Solution for x^2+4x+4=375 equation:


Simplifying
x2 + 4x + 4 = 375

Reorder the terms:
4 + 4x + x2 = 375

Solving
4 + 4x + x2 = 375

Solving for variable 'x'.

Reorder the terms:
4 + -375 + 4x + x2 = 375 + -375

Combine like terms: 4 + -375 = -371
-371 + 4x + x2 = 375 + -375

Combine like terms: 375 + -375 = 0
-371 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '371' to each side of the equation.
-371 + 4x + 371 + x2 = 0 + 371

Reorder the terms:
-371 + 371 + 4x + x2 = 0 + 371

Combine like terms: -371 + 371 = 0
0 + 4x + x2 = 0 + 371
4x + x2 = 0 + 371

Combine like terms: 0 + 371 = 371
4x + x2 = 371

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 = 371 + 4

Reorder the terms:
4 + 4x + x2 = 371 + 4

Combine like terms: 371 + 4 = 375
4 + 4x + x2 = 375

Factor a perfect square on the left side:
(x + 2)(x + 2) = 375

Calculate the square root of the right side: 19.364916731

Break this problem into two subproblems by setting 
(x + 2) equal to 19.364916731 and -19.364916731.

Subproblem 1

x + 2 = 19.364916731 Simplifying x + 2 = 19.364916731 Reorder the terms: 2 + x = 19.364916731 Solving 2 + x = 19.364916731 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 = 19.364916731 + -2 Combine like terms: 2 + -2 = 0 0 + x = 19.364916731 + -2 x = 19.364916731 + -2 Combine like terms: 19.364916731 + -2 = 17.364916731 x = 17.364916731 Simplifying x = 17.364916731

Subproblem 2

x + 2 = -19.364916731 Simplifying x + 2 = -19.364916731 Reorder the terms: 2 + x = -19.364916731 Solving 2 + x = -19.364916731 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 = -19.364916731 + -2 Combine like terms: 2 + -2 = 0 0 + x = -19.364916731 + -2 x = -19.364916731 + -2 Combine like terms: -19.364916731 + -2 = -21.364916731 x = -21.364916731 Simplifying x = -21.364916731

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.364916731, -21.364916731}

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