Question

Solve 6(x-2) ^2 + 7 = 223

Answer 1

Answer:

x = 8 or -4

Step-by-step explanation:

6(x - 2)² + 7 = 223

PEMDAS

expand (x - 2)² first using FOIL

(x - 2)(x - 2)

x² - 2x - 2x + 4

x² - 4x + 4

rewrite equation

6(x² - 4x + 4) + 7 = 223

distribute the 6 through the parentheses

6x² - 24x + 24

rewrite equation

6x² - 24x + 24 + 7 = 223

combine like terms

6x² - 24x + 31 = 223

subtract both sides by 223

6x² - 24x - 192 = 0

divide both sides by 6

x² - 4x - 32 = 0

factor with factoring X

x² - 8x + 4x - 32 = 0

factor by grouping

(x² - 8x) + (4x - 32) = 0

x(x - 8) +4 (x - 8) = 0

(x - 8)(x + 4) = 0

x = 8 or -4

Answer 2

Answer:

x= -4,or x=8

Step-by-step explanation:

$6(x-2) ^2 + 7 = 223\\=>6(x^{2} -4x+4)+7=223\\=>6x^{2} -24x+24+7=223\\=>6x^{2} -24x+31=223\\=>6x^{2} -24x=223-31\\=>6x^{2} -24x=192\\=>6x^{2} -24x-192=0\\=>x^{2} -4x-32=0\\=>x^{2} -8x+4x-32=0\\=>x(x-8)+4(x-8)=0\\=>(x-8)(x+4)=0\\x=-4,+8$