x^2-36=3x

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Solution for x^2-36=3x equation:


Simplifying
x2 + -36 = 3x

Reorder the terms:
-36 + x2 = 3x

Solving
-36 + x2 = 3x

Solving for variable 'x'.

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

Combine like terms: 3x + -3x = 0
-36 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -3x + 36 + x2 = 0 + 36

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

Combine like terms: -36 + 36 = 0
0 + -3x + x2 = 0 + 36
-3x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-3x + x2 = 36

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 36 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 36 + 2.25

Combine like terms: 36 + 2.25 = 38.25
2.25 + -3x + x2 = 38.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(x + -1.5) equal to 6.184658438 and -6.184658438.

Subproblem 1

x + -1.5 = 6.184658438 Simplifying x + -1.5 = 6.184658438 Reorder the terms: -1.5 + x = 6.184658438 Solving -1.5 + x = 6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 6.184658438 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 6.184658438 + 1.5 x = 6.184658438 + 1.5 Combine like terms: 6.184658438 + 1.5 = 7.684658438 x = 7.684658438 Simplifying x = 7.684658438

Subproblem 2

x + -1.5 = -6.184658438 Simplifying x + -1.5 = -6.184658438 Reorder the terms: -1.5 + x = -6.184658438 Solving -1.5 + x = -6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -6.184658438 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -6.184658438 + 1.5 x = -6.184658438 + 1.5 Combine like terms: -6.184658438 + 1.5 = -4.684658438 x = -4.684658438 Simplifying x = -4.684658438

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.684658438, -4.684658438}

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