0.5x^2+3x-36=0

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Solution for 0.5x^2+3x-36=0 equation:


Simplifying
0.5x2 + 3x + -36 = 0

Reorder the terms:
-36 + 3x + 0.5x2 = 0

Solving
-36 + 3x + 0.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.5'.
-72 + 6x + x2 = 0

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 6x + 72 + x2 = 0 + 72

Reorder the terms:
-72 + 72 + 6x + x2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 6x + x2 = 0 + 72
6x + x2 = 0 + 72

Combine like terms: 0 + 72 = 72
6x + x2 = 72

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 = 72 + 9

Reorder the terms:
9 + 6x + x2 = 72 + 9

Combine like terms: 72 + 9 = 81
9 + 6x + x2 = 81

Factor a perfect square on the left side:
(x + 3)(x + 3) = 81

Calculate the square root of the right side: 9

Break this problem into two subproblems by setting 
(x + 3) equal to 9 and -9.

Subproblem 1

x + 3 = 9 Simplifying x + 3 = 9 Reorder the terms: 3 + x = 9 Solving 3 + x = 9 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 = 9 + -3 Combine like terms: 3 + -3 = 0 0 + x = 9 + -3 x = 9 + -3 Combine like terms: 9 + -3 = 6 x = 6 Simplifying x = 6

Subproblem 2

x + 3 = -9 Simplifying x + 3 = -9 Reorder the terms: 3 + x = -9 Solving 3 + x = -9 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 = -9 + -3 Combine like terms: 3 + -3 = 0 0 + x = -9 + -3 x = -9 + -3 Combine like terms: -9 + -3 = -12 x = -12 Simplifying x = -12

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6, -12}

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