x^2-48x+36=0

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Solution for x^2-48x+36=0 equation:


Simplifying
x2 + -48x + 36 = 0

Reorder the terms:
36 + -48x + x2 = 0

Solving
36 + -48x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -48x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + -48x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -48x + x2 = 0 + -36
-48x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
-48x + x2 = -36

The x term is -48x.  Take half its coefficient (-24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
-48x + 576 + x2 = -36 + 576

Reorder the terms:
576 + -48x + x2 = -36 + 576

Combine like terms: -36 + 576 = 540
576 + -48x + x2 = 540

Factor a perfect square on the left side:
(x + -24)(x + -24) = 540

Calculate the square root of the right side: 23.237900077

Break this problem into two subproblems by setting 
(x + -24) equal to 23.237900077 and -23.237900077.

Subproblem 1

x + -24 = 23.237900077 Simplifying x + -24 = 23.237900077 Reorder the terms: -24 + x = 23.237900077 Solving -24 + x = 23.237900077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 23.237900077 + 24 Combine like terms: -24 + 24 = 0 0 + x = 23.237900077 + 24 x = 23.237900077 + 24 Combine like terms: 23.237900077 + 24 = 47.237900077 x = 47.237900077 Simplifying x = 47.237900077

Subproblem 2

x + -24 = -23.237900077 Simplifying x + -24 = -23.237900077 Reorder the terms: -24 + x = -23.237900077 Solving -24 + x = -23.237900077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = -23.237900077 + 24 Combine like terms: -24 + 24 = 0 0 + x = -23.237900077 + 24 x = -23.237900077 + 24 Combine like terms: -23.237900077 + 24 = 0.762099923 x = 0.762099923 Simplifying x = 0.762099923

Solution

The solution to the problem is based on the solutions from the subproblems. x = {47.237900077, 0.762099923}

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