Answer: x=2 or x=-12
Step-by-step explanation: Subtract 12 to both sides of the equation: x² + 10x = 24. Subtract 24 to both sides of the equation: x² + 10x -24. Next, find out which two numbers multiply to -24 and add up to 10: 12 and -2.
X² + 12x + -2x -24.
X(x - 2) and 12(x - 2)
Solve for x: (x+12) and (x-2) = 0
X = -12 or x=2
Answer: The correct option is
(A) x = -12 or x = 2.
Step-by-step explanation: We are given to solve the following quadratic equation for x :
[tex]x^2+10x+12=36~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
From equation (i), we have
[tex]x^2+10x+12=36\\\\\Rightarrow x^2+10x+12-36=0\\\\\Rightarrow x^2+10x-24=0\\\\\Rightarrow x^2+12x-2x-24=0~~~~~~~[\textup{the sum of 12 and -2 is 10 and product is -24}]\\\\\Rightarrow x(x+12)-2(x+12)=0\\\\\Rightarrow (x+12)(x-2)=0\\\\\Rightarrow x+12=0,~~~~x-2=0\\\\\Rightarrow x=-12,2.[/tex]
Thus, the required solution of the given equation is x = -12 or x = 2.
Option (A) is CORRECT.
