Question

4(5x + 9)^2 – 33 = -21

Answer 1

Answer:

x = sqrt(3)/5 - 9/5 or x = -9/5 - sqrt(3)/5

Step-by-step explanation by completing the square:

Solve for x over the real numbers:

4 (5 x + 9)^2 - 33 = -21

Add 33 to both sides:

4 (5 x + 9)^2 = 12

Divide both sides by 4:

(5 x + 9)^2 = 3

Take the square root of both sides:

5 x + 9 = sqrt(3) or 5 x + 9 = -sqrt(3)

Subtract 9 from both sides:

5 x = sqrt(3) - 9 or 5 x + 9 = -sqrt(3)

Divide both sides by 5:

x = sqrt(3)/5 - 9/5 or 5 x + 9 = -sqrt(3)

Subtract 9 from both sides:

x = sqrt(3)/5 - 9/5 or 5 x = -9 - sqrt(3)

Divide both sides by 5:

Answer:  x = sqrt(3)/5 - 9/5 or x = -9/5 - sqrt(3)/5

Answer 2

Let’s do this problem step by step.
In the order of PEMDAS, you have to solve the parenthesis first.
Since there’s an X, you have to DISTRIBUTE the 4 into the 5x and the 9.
4•5x= 20x.
4•9=36.
Now, we do the exponents.
The 9 is by the 2, so 9•9=81. Our new equation should look like this:

20x+81-33=-21

Now, we combine the like terms, which are 81 and -33. 81-33= 48. Our new equation should look like this:

20x+48=-21

Now, we have to use the property of subtraction of equality, so we have to subtract 48 from -21, which is -69. Now we have our new equation:

20x=-69

Now we divide -69 by 20

X=-3.45