SOLUTION: Solve by completing the square. Show your work.[please]
29. 2x2 - 6x + 1 = 0
30. -x2 - 8x + 5 = 0
31. 9x2 - 18x - 1 = 0
32. -4x2 + 8x - 3 = 0
Algebra.Com
Question 177853: Solve by completing the square. Show your work.[please]
29. 2x2 - 6x + 1 = 0
30. -x2 - 8x + 5 = 0
31. 9x2 - 18x - 1 = 0
32. -4x2 + 8x - 3 = 0
Found 2 solutions by jim_thompson5910, gonzo:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first two to get you started
29)
Start with the given expression.
Factor out the coefficient . This step is very important: the coefficient must be equal to 1.
Take half of the coefficient to get . In other words, .
Now square to get . In other words,
Now add and subtract inside the parenthesis. Make sure to place this after the "x" term. Notice how . So the expression is not changed.
Group the first three terms.
Factor to get .
Combine like terms.
Distribute.
Multiply.
So after completing the square, transforms to . So .
So is equivalent to .
------------------------------------
Now let's solve
Start with the given equation.
Add to both sides.
Combine like terms.
Divide both sides by .
Reduce.
Take the square root of both sides.
or Break up the "plus/minus" to form two equations.
or Simplify the square root.
or Add to both sides.
or Combine the fractions.
--------------------------------------
Answer:
So the solutions are or .
30)
Start with the given expression.
Factor out the coefficient . This step is very important: the coefficient must be equal to 1.
Take half of the coefficient to get . In other words, .
Now square to get . In other words,
Now add and subtract inside the parenthesis. Make sure to place this after the "x" term. Notice how . So the expression is not changed.
Group the first three terms.
Factor to get .
Combine like terms.
Distribute.
So after completing the square, transforms to . So .
So is equivalent to .
-------------------------------------------------
Now let's solve
Start with the given equation.
Subtract from both sides.
Combine like terms.
Divide both sides by .
Reduce.
Take the square root of both sides.
or Break up the "plus/minus" to form two equations.
or Subtract from both sides.
--------------------------------------
Answer:
So the solutions are or .
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
equation # 29 is: ******************************************************
standard form of the equation is:
ax^2 + bx + c = 0
this is already in standard form.
a term = 2
b term = (-6)
c term = 1
---
first you move the constant to the right side of the equation by subtracting 1 from both sides of the equation to get :
---
you then divide both sides of the equation by 2 to get:
---
you then take half of 3 and factor the left side of the equation to get:
this takes a little explaining.
start of explanation.
here's an example (not anything to do with this problem because the numbers are changed to make it simple).
take .
if you take half the 2 and make this equal to , the answer will be:
that is extra, so you have to subtract it to keep the original equality intact.
you get:
which is what you started off with.
this is exactly what we did above:
we took and factored it to get:
if you do the multiplication, you will see that:
end of explanation.
---
you then add the (3/2)^2 term to both sides of the equation to get:
---
you then take the square root of both sides of the equation to get:
= +/-
---
you then add ((3/2)) to both sides of the equation to get:
x = +/-
---
after doing the math (i used a calculator), you will get:
x = 2.8228...
or
x = .1771...
---
to prove these values are correct, substitute them in the original equation (again i used the calculator with the full rather than the truncated values)
i took the original equation of 2x^2 - 6x + 1 = 0
and substituted these values to get:
0 = 0 both times proving both values are good.
---
equation number 32 is: ***********************************************
standard form of the equation is:
ax^2 + bx + c = 0
this is already in standard form.
a term = -4
b term = 8
c term = -3
---
first you move the constant to the right side of the equation by adding 3 to both sides of the equation to get :
---
you then divide both sides of the equation by (-4) to get:
---
you then take half of 2 and factor the left side of the equation to get:
---
you then add the (1)^2 term to both sides of the equation to get:
---
you then take the square root of both sides of the equation to get:
= +/-
---
you then add 1 to both sides of the equation to get:
x = +/-
---
after doing the math (i used a calculator), you will get:
x = 1.5
or
x = .5
---
to prove these values are correct, substitute them in the original equation (again i used the calculator with the full rather than the truncated values)
i took the original equation of -4x^2 + 8x - 3 = 0
and substituted these values to get:
0 = 0 both times proving both values are good.
---
i will do number 30 next and i will leave number 31 for you to do.
if you follow the steps and understand what is going on, you should be able to complete it.
---
equation number 30 is: **************************************************
standard form of the equation is:
ax^2 + bx + c = 0
this is already in standard form.
a term is -1.
b term is -8.
c term is 5
---
first you move the constant to the right side of the equation by subtracting 5 from both sides of the equation to get :
---
you then divide both sides of the equation by -1 to get:
---
you then take half of 8 and factor the left side of the equation to get:
---
you then add the 4^2 term to both sides of the equation to get:
---
you then take the square root of both sides of the equation to get:
---
you then subtract 4 from both sides of the equation to get:
x = +/-
---
after doing the math (i used a calculator), you will get:
x = .5828...
or
x = =-8.5825...
---
to prove these values are correct, substitute them in the original equation (again i used the calculator with the full rather than the truncated values)
i took the original equation of -x^2 - 8x + 5 = 0
and substituted these values to get:
0 = 0 both times proving both values are good.
---
by now, you should be able to do number 31 by yourself.
let me know if you are having problems.
RELATED QUESTIONS
Solve by completing the square. Show your work.
29. 2x2 - 6x + 1 = 0
30. -x2 -... (answered by edjones)
1. Which of the following is a quadratic equation that has roots of 2 1/2 and 2/3?
A)... (answered by Alan3354)
Complete the square.
1. x2 + 60x +
2. x2 – 7x +
Solve each... (answered by solver91311)
. Solve quadratic equation by completing the square.
4x2 + 8x + 1 = 0
(answered by Nate)
. Solve quadratic equation by completing the square.
4x2 + 8x + 1 = 0
(answered by Nate)
I've missed a lot of school because I've been sick and I'm trying to get all of my work... (answered by jsmallt9)
Solve by completing the square:
x2 + 8x + 13 = 0
Show in steps please
(answered by Earlsdon)
Solve by Factorization
1. x2 - 13x + 30 = 0
2. 2x2 - 3x = 2
3. 3x2 - 7x - 6 = 0 (answered by Alan3354)
Solve by completing the square:
x2 + 8x + 13 = 0
(answered by stanbon)