x^2+400=24x+8

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Solution for x^2+400=24x+8 equation:


Simplifying
x2 + 400 = 24x + 8

Reorder the terms:
400 + x2 = 24x + 8

Reorder the terms:
400 + x2 = 8 + 24x

Solving
400 + x2 = 8 + 24x

Solving for variable 'x'.

Reorder the terms:
400 + -8 + -24x + x2 = 8 + 24x + -8 + -24x

Combine like terms: 400 + -8 = 392
392 + -24x + x2 = 8 + 24x + -8 + -24x

Reorder the terms:
392 + -24x + x2 = 8 + -8 + 24x + -24x

Combine like terms: 8 + -8 = 0
392 + -24x + x2 = 0 + 24x + -24x
392 + -24x + x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
392 + -24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-392' to each side of the equation.
392 + -24x + -392 + x2 = 0 + -392

Reorder the terms:
392 + -392 + -24x + x2 = 0 + -392

Combine like terms: 392 + -392 = 0
0 + -24x + x2 = 0 + -392
-24x + x2 = 0 + -392

Combine like terms: 0 + -392 = -392
-24x + x2 = -392

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -392 + 144

Reorder the terms:
144 + -24x + x2 = -392 + 144

Combine like terms: -392 + 144 = -248
144 + -24x + x2 = -248

Factor a perfect square on the left side:
(x + -12)(x + -12) = -248

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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