300=x^2+6x

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Solution for 300=x^2+6x equation:


Simplifying
300 = x2 + 6x

Reorder the terms:
300 = 6x + x2

Solving
300 = 6x + x2

Solving for variable 'x'.

Reorder the terms:
300 + -6x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
300 + -6x + -1x2 = 0 + x2 + -1x2
300 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
300 + -6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-300 + 6x + x2 = 0

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + 6x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + 6x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + 6x + x2 = 0 + 300
6x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
6x + x2 = 300

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 = 300 + 9

Reorder the terms:
9 + 6x + x2 = 300 + 9

Combine like terms: 300 + 9 = 309
9 + 6x + x2 = 309

Factor a perfect square on the left side:
(x + 3)(x + 3) = 309

Calculate the square root of the right side: 17.578395831

Break this problem into two subproblems by setting 
(x + 3) equal to 17.578395831 and -17.578395831.

Subproblem 1

x + 3 = 17.578395831 Simplifying x + 3 = 17.578395831 Reorder the terms: 3 + x = 17.578395831 Solving 3 + x = 17.578395831 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 = 17.578395831 + -3 Combine like terms: 3 + -3 = 0 0 + x = 17.578395831 + -3 x = 17.578395831 + -3 Combine like terms: 17.578395831 + -3 = 14.578395831 x = 14.578395831 Simplifying x = 14.578395831

Subproblem 2

x + 3 = -17.578395831 Simplifying x + 3 = -17.578395831 Reorder the terms: 3 + x = -17.578395831 Solving 3 + x = -17.578395831 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 = -17.578395831 + -3 Combine like terms: 3 + -3 = 0 0 + x = -17.578395831 + -3 x = -17.578395831 + -3 Combine like terms: -17.578395831 + -3 = -20.578395831 x = -20.578395831 Simplifying x = -20.578395831

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.578395831, -20.578395831}

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