Chapter 9: Q. 9.52 (page 894)

Solve by using the Quadratic Formula: $\frac{1}{9} d^{2} - \frac{1}{2} d = - \frac{1}{3}$

Short Answer

Expert verified

The solution of the quadratic equation is $d = \frac{9 \pm \sqrt{33}}{4}$

Step by step solution

Given information

We are given a quadratic equation $\frac{1}{9} d^{2} - \frac{1}{2} d = - \frac{1}{3}$

Multiply BY LCD and simplify

we get

$18 (\frac{1}{9} d^{2} - \frac{1}{2} d) = 18 (- \frac{1}{3}) 2 d^{2} - 9 d = - 6$

Add 6 on both sides and identify the values of a,b,c

We get,

$2 d^{2} - 9 d + 6 = 0$

On comparing with standard equation we get $a = 2, b = - 9, c = 6$

Write quadratic formula and substitute the values in it

The quadratic formula can be given as

$d = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

On substituting the values we get

$d = \frac{9 \pm \sqrt{81 - 4 (2) (6)}}{2 (2)}$

Simplify

We have,

$d = \frac{9 \pm \sqrt{81 - 48}}{4} d = \frac{9 \pm \sqrt{33}}{4}$

Conclusion

The solution of the quadratic equation is $d = \frac{9 \pm \sqrt{33}}{4}$

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Solve by using the Quadratic Formula: $\frac{1}{9} d^{2} - \frac{1}{2} d = - \frac{1}{3}$

Short Answer

Step by step solution

Given information

Multiply BY LCD and simplify

Add 6 on both sides and identify the values of a,b,c

Write quadratic formula and substitute the values in it

Simplify

Conclusion

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Solve by using the Quadratic Formula:19d2-12d=-13

Short Answer

Step by step solution

Given information

Multiply BY LCD and simplify

Add 6 on both sides and identify the values of a,b,c

Write quadratic formula and substitute the values in it

Simplify

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Solve by using the Quadratic Formula: $\frac{1}{9} d^{2} - \frac{1}{2} d = - \frac{1}{3}$