Question

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

Answer 1

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 $ax^2+bx+c=0$ where a,b,c are coefficients and x is variable .

Here. given: $(x-2)(x+5)=18$

Using rule (Multiplication is distributive over addition) : $a(b+c)=ab+ac$ ,

we can write this equation as,

$(x-2)(x+5) =18\\ x(x+5)-2(x+5) =18\\ x^2+5x-2x-10 =18\\ x^2+3x-10-18 =0\\ x^2+3x-28 =0$

On comparing this equation with $x^2$ - (sum of roots)$x$+(product of roots) = 0, we get

sum of roots=3 (7-4)

product of roots = -28 $\left ( 7\times -4 \right )$

Using this fact , we can write this equation as ,

$x^2+7x-4x-28=0\\x\left ( x+7 \right )-4\left ( x+7 \right )=0\\\left ( x-4 \right )\left ( x+7 \right )=0\\\Rightarrow x=4\,,\,x=-7$

Answer 2

Hello!

Answer:

$\boxed{x=4, x=-7}\checkmark$

Step-by-step explanation:

First, expand.

$x^2+3x-10=18$

Then, subtract by 18 both sides.

$x^2+3x-10-18=18-18$

Simplify and solve.

$x^2+3x-28=0$

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!

Have a nice day! :)

Thank you!