SOLUTION: I NEED SOME HELP WITH SOME PROBLEMS ON QUADRATIC EQUATIONS.... 1) (2+X)SQUARED=49 2) (X+2)(3X-4)=(X+5)(2X-5) 3)CAN NOT TELL IF THE EQUATION IS RATIONAL OR IRRATIONAL...8XSQUA

Question 105663This question is from textbook college algebra
: I NEED SOME HELP WITH SOME PROBLEMS ON QUADRATIC EQUATIONS....
1) (2+X)SQUARED=49
2) (X+2)(3X-4)=(X+5)(2X-5)
3)CAN NOT TELL IF THE EQUATION IS RATIONAL OR IRRATIONAL...8XSQUARED=14X-3
4)S=SO+GTSQUARED+K FOR T WITH THE DENOMINATOR OF 0
This question is from textbook college algebra

Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
1) (2+X)SQUARED=49
find square root on both sides

2) multiply terms on both sides
add like terms on both sides

add to both sides

add to both sides

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-3, and c=17

Negate -3 to get 3

Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

After simplifying, the quadratic has roots of

or

3)EQUATION IS RATIONAL....8XSQUARED=14X-3

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=8, b=-14, and c=3

Negate -14 to get 14

Square -14 to get 196 (note: remember when you square -14, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 8 to get 16

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator

Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator

Divide

So another answer is

So our solutions are:

or

4)S=SO+GTSQUARED+K FOR T WITH THE DENOMINATOR OF 0

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