4x+5=x^2-27

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Solution for 4x+5=x^2-27 equation:


Simplifying
4x + 5 = x2 + -27

Reorder the terms:
5 + 4x = x2 + -27

Reorder the terms:
5 + 4x = -27 + x2

Solving
5 + 4x = -27 + x2

Solving for variable 'x'.

Reorder the terms:
5 + 27 + 4x + -1x2 = -27 + x2 + 27 + -1x2

Combine like terms: 5 + 27 = 32
32 + 4x + -1x2 = -27 + x2 + 27 + -1x2

Reorder the terms:
32 + 4x + -1x2 = -27 + 27 + x2 + -1x2

Combine like terms: -27 + 27 = 0
32 + 4x + -1x2 = 0 + x2 + -1x2
32 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
32 + 4x + -1x2 = 0

Factor a trinomial.
(8 + -1x)(4 + x) = 0

Subproblem 1

Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Subproblem 2

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Solution

x = {8, -4}

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