Math Help!!!!!?

Question

I don't understand how to answer the following questions:
x^2 = x + 6
Answer: x = 3 or -2

x^2 = 3x + 70
Answer: x = 10 or -7

x^2 + 12 = 7x
Answer: x = 3 or 4

2x^2 + 2 = 5x
Answer: x = 1/2 or 2

3x^2 + 17x + 20 = 0
Answer: x = -4 or -5/3

2x^2 + 5 = 11x
Answer: x = 1/2 or 5

3x^2 + 13x + 4 = 0
Answer: -1/3 or -4

2x^2 + 17x = 9
Answer: x = 1/2 or -9

3x^2 + 2x = 8
Answer: x = 4/3 or -2

Answer 1

Plug each value of x into the equation to determine which value solves the equation.

X^2=x + 6 (X^2 is x squared)
3^2=3+6
9=9

-2^2= -2+6
4=4
So both 3 or -2 work

Answer 2

Let me do just a few and hope you can get the idea from that. Let's take the first one:

x^2=x+6; rewrite in the form:

x^2-x-6=0; factor: (x+2)(x-3)=0. This means that whenever either expression in parentheses is zero, the product will be zero. So, when x=-2, the first parenthesis is zero; when x=3 the second term is zero. therefore, this quadratic equation has two solutions, x=-2,3, since the equation is met whenever x has either of those (but only those values).

Let's do the last one: 3x^2+2x=8 or:

3x^2+2x-8=0 Factor this equation:

(3x-4)(x+2)=0 the first term is zero when x=4/3, the second term is zero when x=-2.

You can apply this method to all the parts of your problem.

Answer 3

I'm going to take a wild guess here and assume you're expected to solve the equations without the answer. To do this, you would have to first set the equations to 0 by moving all the terms to one side.
For the first one:
x^2 = x + 6
x^2 - x - 6 = 0
(x - 3) (x + 2) = 0
x = 3 x = -2

Do that for all of the problems. If you can't figure out how to factor it by just looking at it, you can use the quadratic formula if you have learned that.

Answer 4

Two ways to find the answer Either substitue x with the possibles answers to determine the correct answer or solve the equation

Answer 5

no need to factorize and wtever ... simply replace x in the equation... do them mentally