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

Moncelliqo4

Moncelliqo4

Answered question

2022-11-27

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

Answer & Explanation

CobeBedererKDs

CobeBedererKDs

Beginner2022-11-28Added 6 answers

Answer:
Solution of the given equation: x = 4 , 7
Step-by-step explanation:
An equation is a mathematical statement that states that two things are equal to each other.
A linear equation in one variable is of the form a x 2 + b x + c = 0 where a,b,c are coefficients and x is variable .
Here. given: ( x 2 ) ( x + 5 ) = 18
Using rule (Multiplication is distributive over addition) : a ( b + c ) = a b + b c
we can write this equation as,
( x 2 ) ( x + 5 ) = 18 x ( x + 5 ) 2 ( x + 5 ) = 18 x 2 + 5 x 2 x 10 = 18 x 2 + 3 x 10 18 = 0 x 2 + 3 x 28 = 0
On comparing this equation with x 2 - (sum of roots)+(product of roots) = 0, we get
sum of roots=3 (7-4)
product of roots = -28 ( 7 × 4 )
Using this fact , we can write this equation as ,
x 2 + 7 x 4 x 28 = 0
x 2 + 7 x 4 x 28 = 0 x ( x + 7 ) 4 ( x + 7 ) = 0 ( x 4 ) ( x + 7 ) = 0 x = 4 , x = 7

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