x^2+6x=54

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Solution for x^2+6x=54 equation:


Simplifying
x2 + 6x = 54

Reorder the terms:
6x + x2 = 54

Solving
6x + x2 = 54

Solving for variable 'x'.

Reorder the terms:
-54 + 6x + x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + 6x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + 6x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 6x + x2 = 0 + 54
6x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
6x + x2 = 54

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 = 54 + 9

Reorder the terms:
9 + 6x + x2 = 54 + 9

Combine like terms: 54 + 9 = 63
9 + 6x + x2 = 63

Factor a perfect square on the left side:
(x + 3)(x + 3) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(x + 3) equal to 7.937253933 and -7.937253933.

Subproblem 1

x + 3 = 7.937253933 Simplifying x + 3 = 7.937253933 Reorder the terms: 3 + x = 7.937253933 Solving 3 + x = 7.937253933 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 = 7.937253933 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.937253933 + -3 x = 7.937253933 + -3 Combine like terms: 7.937253933 + -3 = 4.937253933 x = 4.937253933 Simplifying x = 4.937253933

Subproblem 2

x + 3 = -7.937253933 Simplifying x + 3 = -7.937253933 Reorder the terms: 3 + x = -7.937253933 Solving 3 + x = -7.937253933 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 = -7.937253933 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.937253933 + -3 x = -7.937253933 + -3 Combine like terms: -7.937253933 + -3 = -10.937253933 x = -10.937253933 Simplifying x = -10.937253933

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.937253933, -10.937253933}

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