Question

Please help me with this problem please show steps so i know for next time

Answer 1

Answer:  2/3, -4/3

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Explanation:

You could use the AC method to factor this, but the quadratic formula is the most efficient route in my opinion. This will avoid any guess-and-check.

Compare the original equation to the form $a\text{x}^2 + b\text{x} + c = 0$

We have a = 9, b = 6, and c = -8

Those values lead to...

$\text{x} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\text{x} = \frac{-6\pm\sqrt{(6)^2-4(9)(-8)}}{2(9)}\\\\\text{x} = \frac{-6\pm\sqrt{324}}{18}\\\\\text{x} = \frac{-6\pm18}{18}\\\\\text{x} = \frac{-6+18}{18} \ \text{ or } \ \text{x} = \frac{-6-18}{18}\\\\\text{x} = \frac{12}{18} \ \text{ or } \ \text{x} = \frac{-24}{18}\\\\\boldsymbol{\text{x} = \frac{2}{3} \ \text{ or } \ \text{x} = -\frac{4}{3}}$

Side notes:

• 2/3 = 0.667 approximately
• -4/3 = 1.333 approximately
• Since your teacher did not give rounding instructions, I'll assume s/he wants the fraction form of each x value (rather than the decimal form). Be sure to follow all instructions given, and ask for clarification if need.
• To confirm the solutions, replace every copy of x with either 2/3 or -4/3 (pick one value only). Simplifying the left hand side should lead to 0. I'll let you check each answer.