Chapter 9: Q. 9.44 (page 890)

Solve by using the Quadratic Formula: $b^{2} + 24 = - 10 b$

Short Answer

Expert verified

The solution of the above equation is $b = - 4$ and $b = - 6$

Step by step solution

Given information

We are given an quadratic equation $b^{2} + 24 = - 10 b$

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

We get,

$b^{2} + 10 b + 24 = 0$

On comparing with standard form we get

$x = 1, y = 10, z = 24$

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

The quadratic formula can be given as

$b = \frac{- y \pm \sqrt{y^{2} - 4 x z}}{2 x}$

Now we substitute the values of $x, y, z$

We get,role="math" localid="1644928858295" $b = \frac{- 10 \pm \sqrt{100 - 4 (24)}}{2}$

Simplify and find the values of b

We get

$b = \frac{- 10 \pm \sqrt{100 - 4 (24)}}{2} b = \frac{- 10 \pm \sqrt{100 - 96}}{2} b = \frac{- 10 \pm 2}{2}$

b = \frac{- 10 \pm \sqrt{100 - 4 (24)}}{2} b = \frac{- 10 \pm \sqrt{100 - 96}}{2} b = \frac{- 10 \pm 2}{2}

On further simplifying we get

$b = \frac{- 10 + 2}{2} b = \frac{- 8}{2} b = - 4$ and $b = \frac{- 10 - 2}{2} b = \frac{- 12}{2} b = - 6$

Check the solution

We substitute $x = - 4$ in the quadratic equation

$b^{2} + 10 b + 24 {(- 4)}^{2} + 10 (- 4) + 24 16 - 40 + 24 = 0$

Now we substitute $x = - 6$ in the quadratic equation

$b^{2} + 10 b + 24 {(- 6)}^{2} + 10 (- 6) + 24 36 - 60 + 24 = 0$

Conclusion

The solution of the above equation is $b = - 4$ and $b = - 6$

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Solve by using the Quadratic Formula: $b^{2} + 24 = - 10 b$

Short Answer

Step by step solution

Given information

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

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

Simplify and find the values of b

Check the solution

Conclusion

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

Short Answer

Step by step solution

Given information

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

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

Simplify and find the values of b

Check the solution

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

Solve by using the Quadratic Formula: $b^{2} + 24 = - 10 b$