Question

Which is a solution to the equation?
(x −2)(x + 5) = 18

Answer 1

`\huge\boxed{x=-7\ or\ x=4}`

Explanation:

`(x-2)(x+5)=18\qquad\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(x)(x)+(x)(5)+(-2)(x)+(-2)(5)=18\\\\x^2+5x-2x-10=18\qquad\text{subtract 18 from both sides}\\\\x^2+5x-2x-10-18=18-18\qquad\text{combine like terms}\\\\x^2+(5x-2x)+(-10-18)=0\\\\x^2+3x-28=0\\\\x^2+7x-4x-28=0\qquad\text{use the distributive property}\\\\x(x+7)-4(x+7)=0\\\\(x+7)(x-4)=0\iff x+7=0\ \vee\ x-4=0\\\\x+7=0\qquad\text{subtract 7 from both sides}\\x+7-7=0-7\\\boxed{x=-7}\\\\x-4=0\qquad\text{add 4 to both sides}\\x-4+4=0+4\\\boxed{x=4}`

Answer 2

multiply first you will get x^2+5x-2x-10=18

so , x^2+3x-28=0

find the roots , it will be (x+7)(x-4)=0

the answer is -7&4