SOLUTION: Solve by completing the square: x^2 + 6x - 8 = 0 Solve by using the quadratic formula: z^2 -6z -14 = 0 Solve: x^2 + 2x - 8 <or=to 0

Algebra.Com
Question 34247: Solve by completing the square:
x^2 + 6x - 8 = 0

Solve by using the quadratic formula:
z^2 -6z -14 = 0

Solve:
x^2 + 2x - 8
Answer by lyra(94)   (Show Source): You can put this solution on YOUR website!
Solved by pluggable solver: COMPLETING THE SQUARE solver for quadratics
Read this lesson on completing the square by prince_abubu, if you do not know how to complete the square.
Let's convert to standard form by dividing both sides by 1:
We have: . What we want to do now is to change this equation to a complete square . How can we find out values of somenumber and othernumber that would make it work?
Look at : . Since the coefficient in our equation that goes in front of x is 6, we know that 6=2*somenumber, or . So, we know that our equation can be rewritten as , and we do not yet know the other number.
We are almost there. Finding the other number is simply a matter of not making too many mistakes. We need to find 'other number' such that is equivalent to our original equation .


The highlighted red part must be equal to -8 (highlighted green part).

, or .
So, the equation converts to , or .

Our equation converted to a square , equated to a number (17).

Since the right part 17 is greater than zero, there are two solutions:


, or






Answer: x=1.12310562561766, -7.12310562561766.


Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=92 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 7.79583152331272, -1.79583152331272. Here's your graph:


<=0




so answer is (- infinity,2]
Hope this helps,
lyra
RELATED QUESTIONS

Solve by completing the square and quadratic formula: 1.) x^2-6x+8=0... (answered by mananth)
Solve by completing the square. x^2 + 2x – 8 = 0 (answered by jim_thompson5910)
x^2-6x+8=0 Solve using the quadratic... (answered by jim_thompson5910)
Solve the following equations by completing the square. x^2+8x+7=-8 2x^2=7x-15=0... (answered by pvaka)
Solve by completing the square: w^2 - 2w- 15 = 0 Solve x^2 + 2x - 8 < or = to... (answered by checkley71)
Solve by completing the square and quadratic formula. 1.) x^2-6x+8=0 2.) t^2=4-3t 3.)... (answered by josgarithmetic)
solve by completing the square: x^2 + 5x... (answered by checkley77)
Solve by completing the square. x^2 + 6x + 2 =... (answered by Earlsdon)
How to solve this quadratic equation by completing the square x^2 + 6X - 7 =... (answered by longjonsilver)