b^{2}+5=8b−10

pedzenekO 2020-11-26 Answered
b2+5=8b10
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Gennenzip
Answered 2020-11-27 Author has 96 answers

To solve a quadratic equation, we need to first move all the terms to one side.
Subtracting 8b on both sides of b2+5=8+5=8b10 gives b28b+5=10.
Adding 10 on both sides then gives b28b+15=0.
Now that we have all the terms on one side, we want to see if the quadratic is factorable. If it's not factorable, we will need to use the Quadratic Formula to find the solutions.
A quadratic of the form x2+Bx+Cx can be factored to (x+m)(x+n) if there are two numbers, m and n, such that m+n=B and mn=C.
For b28b+15, we then need to see if there are two numbers that multiply to 15 and add to −8. Since 5(3)=15 and 5+(3)=8, then the two numbers will be −5 and −3.
b28b+15b can then factor to (b−5)(b−3).
The equation b28b+15=0 can then be written as (b−5)(b−3)=0.
The Zero Product Property states that if ab=0, then a=0 or b=0. Using this property, if (b5)(b3)=0, we can then say that b−5=0 or b−3=0.
Solving b−5=0 for bb gives b=5. Solving b−3=0 for b gives b=3.
The two solutions of the equation are then b=3 and b=5.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-07-10
Prove:If x is irrational, then n x [ n x ] are distinct for all n Z .
asked 2021-08-13
Solve the equation:
y25=0
asked 2021-06-22

During a test by the editors of an auto magazine, the stopping distance s (in metres) of the MacPherson X-2 racing car conformed to the rule
s=f(t)=40t5t2(t0) where t was the time (in seconds) after the brakes were applied.
a. Find an expression for the car's velocity v at any time t.
b. What was the car's velocity when the brakes were first applied?
c. What was the car's stopping distance for that particular test? Hint: The stopping time is found by setting v=0.

asked 2020-11-02
62
=
A. 36
B. 12
C. 66
D. 30
asked 2020-12-28
Use what you just learned about negative slopes to solve this problem. A storm moves at a rate of 8 miles per hour. It is 200 miles away from Freeport and headed directly for this town. The equation y = 200 - 8x can be used to represent this function. Identify the slope and y-intercept and explain what they represent.
asked 2022-04-23
Given 32(x+3)1=|x+3|+a has exactly two real roots, then the maximum possible value of |[a]| is? ( where [] denotes the greatest integer function )
asked 2021-12-12
Consider the following. (Round your answers to four decimal places.)
f(x,y)=xcos(y)
(a) Find f(7,9) and f(7.1,9.05) and calculate Δz.
f(7,9)=?
f(7.1,9.05)=?
Δz=?
(b) Use the total differential dz to approximate Δz.
dz=?