x^2+28=12x+1

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Solution for x^2+28=12x+1 equation:


Simplifying
x2 + 28 = 12x + 1

Reorder the terms:
28 + x2 = 12x + 1

Reorder the terms:
28 + x2 = 1 + 12x

Solving
28 + x2 = 1 + 12x

Solving for variable 'x'.

Reorder the terms:
28 + -1 + -12x + x2 = 1 + 12x + -1 + -12x

Combine like terms: 28 + -1 = 27
27 + -12x + x2 = 1 + 12x + -1 + -12x

Reorder the terms:
27 + -12x + x2 = 1 + -1 + 12x + -12x

Combine like terms: 1 + -1 = 0
27 + -12x + x2 = 0 + 12x + -12x
27 + -12x + x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
27 + -12x + x2 = 0

Factor a trinomial.
(3 + -1x)(9 + -1x) = 0

Subproblem 1

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Subproblem 2

Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9

Solution

x = {3, 9}

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