Question

Solve for the exact value of the following quadratic !

(x-5)^2-4(x-5)-12=0

THANK YOU

Answer 1

\[(x-5)²-4(x-5)-12=0\]Call x-5 = a, you will have,
\[a²-4a-12=0\]Solve for a using the quadratic equations and you will find a = 6 and a=-2
So, if x-5 = a, you will have:

Answer 2

x-5=6
and
x-5=-2

x=11 and x = 3

Answer 3

Hi I am new here, can you explain to me how do you do this?

Answer 4

Which part?

Answer 5

I mean the equation that you have written above? It would help me to know something new. Because I have never learned calculus before.

Answer 6

The one that says x-5^2 and some stuff like that

Answer 7

This is not calculus, just algebra :]
But, what I did is changing an expression to a variable.
When you have for example:

2(x+3) + 3(x+3) = 5
It's easy to solve, but, you can call x+3 = a, and do:
2a + 3a = 5
5a = 5
a = 1,
So, if x+3 = a, x+3 = 1, x= -2 :]]

Answer 8

The equation that has (x-5)^2 its a quadratic equation. Do you know how to solve that?

Answer 9

Well I know that the x is a variable and the 2 is the exponent that needs to be also considered as to solving the problem. But my weakness is one solving the functions.

Answer 10

Long method.\[\large (x-5)^2-4(x-5)-12=0\]\[\large x^2 - 10x+25 - 4x +20 - 12=0\] Simplify. \[\large x^2 -14x+33 = 0\]\[\large (x-11)(x-3)=0\] Now solve, for each x-value. \[\large x-11=0\]\[\large x-3 = 0\]

Answer 11

For example,
(x-3)² = 9
Do you know how to solve that?

Answer 12

OMG thank you so so much could you help me with one more!?!

a bridge is supported by three arches. The function that describes the arches is h(x) = 0.25x^2 + 2.375x where h(x) is the height, in meters, of the arch above the ground at any distance, x, in meters, from one end of the bridge. How far apart are the bases of each arch?

Answer 13

I think that the x is equaled to 6. So it would be (6-3)^2=9. Am I correct?

Answer 14

This is one of the answers, but when you have a quadratic equation, usually you have two solutions, so
If (x-3)² = 9,
You can take the square root and you will say that
x-3 = +3 or -3
So, x-3 = 3 or x-3 = -3
So, Solutions are x = 6 and x = 0,

Test if x = 0! , You will have (0 - 3)² = (-3)² = 9 !

Answer 15

What is quadratic equation?