Use the discriminant to determine how many real-number solutions the equation has.

1 - 7a² = -7a - 2

1 - 7a² = -7a - 2

Discriminant is b² - 4ac

If b² - 4ac > 0, there are two real number solutions

If b² - 4ac = 0, there is one real number solution

If b² - 4ac < 0, there are two imaginary number solutions

1 - 7a² = -7a - 2

7a² - 7a - 3 = 0 {added 7a² and subtracted 1 from both sides}

a = 7, b = -7, c = -3

b² - 4ac

= (-7)² - 4(7)(-3)

= 49 + 84

= 133

133 > 0,there are

**two real number solutions**

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