X2+11x=-24
I assume by X2 you mean x squared (x^2)?
If so, write as ax^2+bx+c=0:
x^2 +11x +24 =0
in this case, a=1 because x^2 is not multiplied by a constant, b=11 and c=24.
To find the two solutions, use the formula:
x= (-b +�ã4ac)/(2a)
x= (-b -�ã4ac)/(2a)
Amendment: The square root sign was not properly processed by this website, it is supposed to say -b+ square root of 4ac for the first solution and -b- square root of 4ac for the second
Second amendment:
I see more got lost in formatting - this is what you get for using foreign version of Windows, apparently.
x= (-b +- sqrt(b^2 -4ac))/(2a)
Let us hope this works now. Sorry about the mess :-)
To solve the equation x^2 + 11x = -24, we need to rearrange it in order to isolate the variable x on one side of the equation. Here's how we can do it step by step:
Step 1: Move the constant term to the right side of the equation.
x^2 + 11x + 24 = 0
Step 2: Factorize the quadratic equation.
To factorize the quadratic equation, we need to find two numbers that multiply to give 24 and add up to give 11. In this case, the numbers are 3 and 8.
(x + 3)(x + 8) = 0
Step 3: Set each binomial factor equal to zero and solve for x.
x + 3 = 0 or x + 8 = 0
For the first equation, subtract 3 from both sides:
x = -3
For the second equation, subtract 8 from both sides:
x = -8
Step 4: Check the solutions by substituting them back into the original equation.
Substituting x = -3:
(-3)^2 + 11(-3) = -24
9 - 33 = -24
-24 = -24 (True)
Substituting x = -8:
(-8)^2 + 11(-8) = -24
64 - 88 = -24
-24 = -24 (True)
Therefore, the solutions to the equation x^2 + 11x = -24 are x = -3 and x = -8.