x^2-30x+24=0

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Solution for x^2-30x+24=0 equation: 


Simplifying
x2 + -30x + 24 = 0

Reorder the terms:
24 + -30x + x2 = 0

Solving
24 + -30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -30x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -30x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -30x + x2 = 0 + -24
-30x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-30x + x2 = -24

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = -24 + 225

Reorder the terms:
225 + -30x + x2 = -24 + 225

Combine like terms: -24 + 225 = 201
225 + -30x + x2 = 201

Factor a perfect square on the left side:
(x + -15)(x + -15) = 201

Calculate the square root of the right side: 14.177446879

Break this problem into two subproblems by setting 
(x + -15) equal to 14.177446879 and -14.177446879.


Subproblem 1
x + -15 = 14.177446879

Simplifying
x + -15 = 14.177446879

Reorder the terms:
-15 + x = 14.177446879

Solving
-15 + x = 14.177446879

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '15' to each side of the equation.
-15 + 15 + x = 14.177446879 + 15

Combine like terms: -15 + 15 = 0
0 + x = 14.177446879 + 15
x = 14.177446879 + 15

Combine like terms: 14.177446879 + 15 = 29.177446879
x = 29.177446879

Simplifying
x = 29.177446879


Subproblem 2
x + -15 = -14.177446879

Simplifying
x + -15 = -14.177446879

Reorder the terms:
-15 + x = -14.177446879

Solving
-15 + x = -14.177446879

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '15' to each side of the equation.
-15 + 15 + x = -14.177446879 + 15

Combine like terms: -15 + 15 = 0
0 + x = -14.177446879 + 15
x = -14.177446879 + 15

Combine like terms: -14.177446879 + 15 = 0.822553121
x = 0.822553121

Simplifying
x = 0.822553121


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.177446879, 0.822553121}

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