(x+2)(x+2)-48=1

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Solution for (x+2)(x+2)-48=1 equation:


Simplifying
(x + 2)(x + 2) + -48 = 1

Reorder the terms:
(2 + x)(x + 2) + -48 = 1

Reorder the terms:
(2 + x)(2 + x) + -48 = 1

Multiply (2 + x) * (2 + x)
(2(2 + x) + x(2 + x)) + -48 = 1
((2 * 2 + x * 2) + x(2 + x)) + -48 = 1
((4 + 2x) + x(2 + x)) + -48 = 1
(4 + 2x + (2 * x + x * x)) + -48 = 1
(4 + 2x + (2x + x2)) + -48 = 1

Combine like terms: 2x + 2x = 4x
(4 + 4x + x2) + -48 = 1

Reorder the terms:
4 + -48 + 4x + x2 = 1

Combine like terms: 4 + -48 = -44
-44 + 4x + x2 = 1

Solving
-44 + 4x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
-44 + -1 + 4x + x2 = 1 + -1

Combine like terms: -44 + -1 = -45
-45 + 4x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-45 + 4x + x2 = 0

Factor a trinomial.
(-9 + -1x)(5 + -1x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {-9, 5}

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