solve for b?

Question

5b squared minus 5b plus 1 equals 0

Answer 1

Simplifying
5b^2 + -5b + 1 = 0

Reorder the terms:
1 + -5b + 5b^2 = 0

Solving
1 + -5b + 5b^2 = 0

Begin completing the square. Divide all terms by
5 the coefficient of the squared term:

Divide each side by '5'.
0.2 + -1b + b^2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -1b + -0.2 + b^2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -1b + b^2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -1b + b^2 = 0 + -0.2
-1b + b^2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-1b + b^2 = -0.2

The b term is -1b. Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1b + 0.25 + b^2 = -0.2 + 0.25

Reorder the terms:
0.25 + -1b + b^2 = -0.2 + 0.25

Combine like terms: -0.2 + 0.25 = 0.05
0.25 + -1b + b^2 = 0.05

Factor a perfect square on the left side:
(b + -0.5)(b + -0.5) = 0.05

Calculate the square root of the right side: 0.223606798

Break this problem into two subproblems by setting
(b + -0.5) equal to 0.223606798 and -0.223606798.

Subproblem 1b + -0.5 = 0.223606798

Simplifying
b + -0.5 = 0.223606798

Reorder the terms:
-0.5 + b = 0.223606798

Solving
-0.5 + b = 0.223606798

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + b = 0.223606798 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + b = 0.223606798 + 0.5
b = 0.223606798 + 0.5

Combine like terms: 0.223606798 + 0.5 = 0.723606798
b = 0.723606798

Simplifying
b = 0.723606798

Subproblem 2b + -0.5 = -0.223606798

Simplifying
b + -0.5 = -0.223606798

Reorder the terms:
-0.5 + b = -0.223606798

Solving
-0.5 + b = -0.223606798

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + b = -0.223606798 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + b = -0.223606798 + 0.5
b = -0.223606798 + 0.5

Combine like terms: -0.223606798 + 0.5 = 0.276393202
b = 0.276393202

Simplifying
b = 0.276393202

SolutionThe solution to the problem is based on the solutions
from the subproblems.
b = {0.723606798, 0.276393202}

Answer 2

well I hope this is easy for you.
let us use completing the square method
5b^2 - 5b + 1 = 0
1) separate the constant term 1
5b^2 -5b = -1
2) divide both sides by 5
b^2 - b = -1/5
3) complete the square for b
b^2 -b + 1/4 = -1/5 + 1/4
1/4 happens to be that term that could make the left member perfect square.
4) factor the left side and simplify the fraction on the right side
( b - 1/2)^2 = 1/20
5) take square root both sides
( b - 1/2) = + or - (square root of 5) / 10
6) transpose 1/2
b = 1/2 + or - (square root of 5 )/ 10
7) or better yet
b = 5 + or - (the square root of 5) / 10

Answer 3

5b^2 – 5b + 1 = 0 …………………….(1)

Compare this quadratic equation with this basic quadratic equation:-

aX^2 + bX + c = 0 …………………….(2)

In this case, b from first equation is same as X in the second equation.

We have to use the following formula to solve for b from first equation:-

X = [- b ± √ (b^2 – 4ac)] / [2a]

From first equation:-

a = 5
b = -5
c = 1

Substitute all the values of a, b, and c into the given formula:-

X= [- (-5) ± √ ({-5} ^2 – 4*5*1)] / [2*5]
= [5 ± √ (25– 20)] / [10]
= [5 ± √ (5)] / [10]
= [5 + √ (5)] / [10] or [5 - √ (5)] / [10]
= 0.723606797 or 0.276393202

So the solution for b that you looking for is b = X = 0.723606797 or 0.276393202

Answer 4

You will really need to use the quadratic formula...I can't show you the work on here due to computer functionality...the formula is -b plus or minus the square root of b squared-4(a)(c) all over 2a...just a hint, though. your negative b at the beginning will be a positive 5, because your b of abc for the formula is -5 and when you have a negative and negative, it becomes positive. Much luck!

Answer 5

Assuming that when you said 5b squared you meant 5b^2...

First subtract 1 from both sides.

5b^2 - 5b = -1

Then,

5b(b-1) = -1

or

5(b^2-b) = -1

Divide

b^2-b= -1/5

b(b-1)= -1/5

i don't know what next, sorry lol.

Answer 6

is it (5b)^2
or
5 (b^2)
?

it could be 1 or -1/5

Answer 7

(-b +or- root(b^2-4ac))/(2a)
(5 +- root(25-4*5*1))/(10)
b=(5 -root5)/10 or (5+root5)/10

dont listen to them, its deffinately not 1. test it

Answer 8

look up the quadratic equation on the internet and use that. it is fairly easy

Answer 9

5b²-5b+1=0
5b²-5b=-1
5b²=5b-1
b²=(5b-1)/5
b=√((5b-1)/5)

Answer 10

.7236068