SOLUTION: Can someone Please, Please, Please help me solve tis problem by using the Quadratic Formula! I am desperite! Thank You! Solve by Using the Quadratic Formula: x^2 - 7x - 1= -7

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can someone Please, Please, Please help me solve tis problem by using the Quadratic Formula! I am desperite! Thank You! Solve by Using the Quadratic Formula: x^2 - 7x - 1= -7      Log On


   

Question 103931This question is from textbook Intermediate Algebra
: Can someone Please, Please, Please help me solve tis problem by using the Quadratic Formula! I am desperite! Thank You!
Solve by Using the Quadratic Formula:
x^2 - 7x - 1= -7 This question is from textbook Intermediate Algebra

Found 2 solutions by jim_thompson5910, JP:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-+7x+-+1=+-7 Start with the given equation


x%5E2+-+7x+-+1%2B+7=0 Add 7 to both sides


x%5E2+-+7x+%2B6=0 Combine like terms


Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-7%2Ax%2B6=0 ( notice a=1, b=-7, and c=6)





x+=+%28--7+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A6+%29%29%2F%282%2A1%29 Plug in a=1, b=-7, and c=6




x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A6+%29%29%2F%282%2A1%29 Negate -7 to get 7




x+=+%287+%2B-+sqrt%28+49-4%2A1%2A6+%29%29%2F%282%2A1%29 Square -7 to get 49 (note: remember when you square -7, you must square the negative as well. This is because %28-7%29%5E2=-7%2A-7=49.)




x+=+%287+%2B-+sqrt%28+49%2B-24+%29%29%2F%282%2A1%29 Multiply -4%2A6%2A1 to get -24




x+=+%287+%2B-+sqrt%28+25+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%287+%2B-+5%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%287+%2B-+5%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%287+%2B+5%29%2F2 or x+=+%287+-+5%29%2F2


Lets look at the first part:


x=%287+%2B+5%29%2F2


x=12%2F2 Add the terms in the numerator

x=6 Divide


So one answer is

x=6




Now lets look at the second part:


x=%287+-+5%29%2F2


x=2%2F2 Subtract the terms in the numerator

x=1 Divide


So another answer is

x=1


So our solutions are:

x=6 or x=1

Answer by JP(22) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 - 7x - 1= -7
First you must set up the equation in quadratic form. Ax^2+bx+c=0
In order to do that you must first add -7 to the other side to get...
x^2-7x-1+7=0
x^2-7x+6=0
It is now in quadratic form.
x^2=a
-7=b
6=c
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28--7+%2B-+sqrt%28+-7%5E2-4%2A1%2A6+%29%29%2F%282%2A1%29+
You plug all of that into the quadratic formula.
Now you start doing your order of operations.
x+=+%28--7+%2B-+sqrt%28+49-24+%29%29%2F%282%29+
x+=+%28--7+%2B-+sqrt%28+25+%29%29%2F%282%29+
x = (--7 +- 5/(2)
x = (++7 +- 5/(2)
x = (++7 + 5/(2)-------->12/2=6
x = (++7 - 5/(2)-------->2/2=1
So the solution set is...
x=6 or x=1