29.3k views
1 vote
Solve the Quadratic Equation . Show all of your work for full credit. 4x^2− 2x − 5= 0

2 Answers

3 votes
Hope this helps! Don’t mind the part I crossed off.
Solve the Quadratic Equation . Show all of your work for full credit. 4x^2− 2x − 5= 0-example-1
User Ryk
by
7.1k points
2 votes
y = 4x^2 - 2x - 5 = 0
Step One
Put brackets around the first 2 terms. Put the five outside the brackets.

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

Step Two
Treat 4 as a common factor put it on the left bracket.
4(x^2 - 2/4 x) - 5 = 0
4(x^2 - 1/2 x) - 5 = 0

Step Three
Take 1/2 the linear term and square it. -1/2 x is the linear term. Drop the x for this step. Leave 1/2 the linear term squared added inside the brackets.
4(x^2 - 1/2x + (1/2*1/2)^2 ) - 5 = 0

Step Four
-=======
You've got an unbalanced equation. It will not break down to what you started with. You have to adjust it with a number after the five.

4(x^2 - 1/2 x + (1/4)^2 ) - 5 - 4 * (1/4)^2
4(x^2 - 1/2 x + 1/16 ) - 5 - 1/4
4(x^2 - 1/2 x + 1/16 ) - 5 - 1/4
4(x^2 - 1/2 x + 1/16 ) - 21/4

Step five
=======
Express what is inside the brackets as a perfect square.
4(x - 1/4)^2 - 21/4 = 0
This is the vertex form of the equation. Now to get the roots which is what you are after.

Step six
Transfer 21/4 to the right hand side.
4(x - 1/4)^2 = 21/4

Step seven
Divide by 4
(x - 1/4)^2 = 21/16

Step eight
Take the square root of both sides.
x - 1/4 = +/- sqrt(21)/4 Transfer the 1/4 over to the right.
x = [1 +/- sqrt(21) )/ 4

That gives you two answers
x = [1 + sqrt(21) ) / 4 <<<<< sqrt answer
x = 1.3945 <<<<< decimal answer.

or

x = [1 - sqrt(21)] / 4 <<<< sqrt answer
x = - 0.8956 Decimal answer

Comment
If you use the quadratic formula, you get
a = 4
b = - 2
c = - 5

x = [- b +/- sqrt ( b^2 - 4ac) ] / 2a
x = [ 2 +/- sqrt ( (-2)^2 - 4((4)(-5))]/2*4
x = [ 2 +/- sqrt ( 4 + 80 ) ] / 8
x = [2 +/- sqrt (84) ] / 8
x = [2 +/- sqrt (4*21) ] /8
x = [2 +/- 2*sqrt (21) ] / 8
x = 2 [1 +/- sqrt(21)] / 8
x = [1 +/- sqrt(21) ] /4 Now you can look above to decide on your answer
User Rhodee
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories