Hello!
Answer:
[tex]\boxed{x=4, x=-7}\checkmark[/tex]
Step-by-step explanation:
First, expand.
[tex]x^2+3x-10=18[/tex]
Then, subtract by 18 both sides.
[tex]x^2+3x-10-18=18-18[/tex]
Simplify and solve.
[tex]x^2+3x-28=0[/tex]
Therefore, the solution to this equation is x=4, and x=-7.
x=4 and x=-7 is the correct answer.
Hope this helps you!
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Thank you!
Answer:
Solution of the given equation: [tex]x=4 , -7[/tex]
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 [tex]ax^2+bx+c=0[/tex] where a,b,c are coefficients and x is variable .
Here. given: [tex](x-2)(x+5)=18[/tex]
Using rule (Multiplication is distributive over addition) : [tex]a(b+c)=ab+ac[/tex] ,
we can write this equation as,
[tex](x-2)(x+5) =18\\ x(x+5)-2(x+5) =18\\ x^2+5x-2x-10 =18\\ x^2+3x-10-18 =0\\ x^2+3x-28 =0\\[/tex]
On comparing this equation with [tex]x^2[/tex] - (sum of roots)[tex] x [/tex]+(product of roots) = 0, we get
sum of roots=3 (7-4)
product of roots = -28 [tex]\left ( 7\times -4 \right )[/tex]
Using this fact , we can write this equation as ,
[tex]x^2+7x-4x-28=0\\x\left ( x+7 \right )-4\left ( x+7 \right )=0\\\left ( x-4 \right )\left ( x+7 \right )=0\\\Rightarrow x=4\,,\,x=-7[/tex]
