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Chapter 9: Q. 9.44 (page 890)

Solve by using the Quadratic Formula:b2+24=-10b

Short Answer

Expert verified

The solution of the above equation isb=-4andb=-6

Step by step solution

01

Given information

We are given an quadratic equationb2+24=-10b

02

Write the equation in standard form by adding 10bto each side. and identify the values of x,y,z

We get,

b2+10b+24=0

On comparing with standard form we get

x=1,y=10,z=24

03

Write quadratic formula and substitute the values of x,y,z

The quadratic formula can be given as

b=-y卤y2-4xz2x

Now we substitute the values of x,y,z

We get,role="math" localid="1644928858295" b=-10卤100-4(24)2

04

Simplify and find the values of b

We get

b=-10卤100-4(24)2b=-10卤100-962b=-10卤22

b=-10卤100-4(24)2b=-10卤100-962b=-10卤22

On further simplifying we get

b=-10+22b=-82b=-4andb=-10-22b=-122b=-6

05

Check the solution

We substitute x=-4in the quadratic equation

b2+10b+24(-4)2+10(-4)+2416-40+24=0

Now we substitute x=-6in the quadratic equation

b2+10b+24(-6)2+10(-6)+2436-60+24=0

06

Conclusion

The solution of the above equation isb=-4andb=-6

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