X*a = 244 is equation (1)
x+a = 2 is equation (2)

Solve equation (2) for 'a' to get
x+a = 2
a = 2-x
Call this equation (3)

We will plug equation (3) into equation (1)
x*a = 244
x*(a) = 244
x*(2-x) = 244
Notice how the 'a' is replaced with an expression in terms of x

Let's solve for x
x*(2-x) = 244
2x-x^2 = 244
x^2-2x+244 = 0

If we use the discriminant formula, d = b^2 - 4ac, then we find that...
d = b^2 - 4ac
d = (-2)^2 - 4*1*244
d = -972
indicating that there are no real number solutions to the equation x^2-2x+244 = 0

So this means that 'x' and 'a' in those two original equations are non real numbers. If you haven't learned about complex numbers yet, then the answer is simply "no solution". At this point you would stop here.

If you have learned about complex numbers, then the solution set is approximately
{x = 1 + 15.588i, a = 1 - 15.588i}
which can be found through the quadratic formula

Note: it's possible that there's a typo somewhere in the problem that your teacher gave you.

6 0

3 years ago

<img src="https://tex.z-dn.net/?f=%28%20%5Cfrac%7B1%7D%7B2%7D%20%20%7Ba%7D%5E%7B2%7D%20%20%2B%20%20%20%5Cfrac%7B1%7D%7B2%7D%20ab

Zigmanuir [339]

Answer:

$\frac{1}{2}$ (a + 2b)(a - b)

Step-by-step explanation:

Assuming you require the expression to be factored

Given

$\frac{1}{2}$ a² + $\frac{1}{2}$ ab - b² ← factor out $\frac{1}{2}$ from each term

= $\frac{1}{2}$ (a² + ab - 2b²) ← factor the quadratic

Consider the factors of the coefficient of the b² term(- 2) which sum to give the coefficient of the ab- term (+ 1)

The factors are + 2 and - 1, since

2 × - 1 = - 2 and 2 - 1 = + 1, thus

a² + ab - 2b² = (a + 2b)(a - b) and

$\frac{1}{2}$ a² + $\frac{1}{2}$ ab - b² = $\frac{1}{2}$ (a + 2b)(a - b)

5 0

3 years ago

The given equation is either linear or equivalent to a linear equation. solve the equation. (if there is no solution, enter no s

murzikaleks [220]

2x+12=33
2x=21
x=10.5
The answer is 10.5

6 0

3 years ago