x^2+2x+1+4x-64=0

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Solution for x^2+2x+1+4x-64=0 equation:


Simplifying
x2 + 2x + 1 + 4x + -64 = 0

Reorder the terms:
1 + -64 + 2x + 4x + x2 = 0

Combine like terms: 1 + -64 = -63
-63 + 2x + 4x + x2 = 0

Combine like terms: 2x + 4x = 6x
-63 + 6x + x2 = 0

Solving
-63 + 6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '63' to each side of the equation.
-63 + 6x + 63 + x2 = 0 + 63

Reorder the terms:
-63 + 63 + 6x + x2 = 0 + 63

Combine like terms: -63 + 63 = 0
0 + 6x + x2 = 0 + 63
6x + x2 = 0 + 63

Combine like terms: 0 + 63 = 63
6x + x2 = 63

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 63 + 9

Reorder the terms:
9 + 6x + x2 = 63 + 9

Combine like terms: 63 + 9 = 72
9 + 6x + x2 = 72

Factor a perfect square on the left side:
(x + 3)(x + 3) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(x + 3) equal to 8.485281374 and -8.485281374.

Subproblem 1

x + 3 = 8.485281374 Simplifying x + 3 = 8.485281374 Reorder the terms: 3 + x = 8.485281374 Solving 3 + x = 8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 8.485281374 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.485281374 + -3 x = 8.485281374 + -3 Combine like terms: 8.485281374 + -3 = 5.485281374 x = 5.485281374 Simplifying x = 5.485281374

Subproblem 2

x + 3 = -8.485281374 Simplifying x + 3 = -8.485281374 Reorder the terms: 3 + x = -8.485281374 Solving 3 + x = -8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -8.485281374 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.485281374 + -3 x = -8.485281374 + -3 Combine like terms: -8.485281374 + -3 = -11.485281374 x = -11.485281374 Simplifying x = -11.485281374

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.485281374, -11.485281374}

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