Use the discriminant to determine how many and what kind of solutions the quadratic equation x2−x=−14 has.

see explanation

Step-by-step explanation:

Given a quadratic equation in standard form : ax² + bx + c = 0 ( a ≠ 0 )

Then the discriminant Δ = b² - 4ac determines the type of solutions

• If b² - 4ac > 0 then roots are real and distinct

• If b² - 4ac = 0 then roots are real and equal

• If b² - 4ac < 0 then roots are not real

Given

x² - x = - 14 ( add 14 to both sides )

x² - x + 14 = 0 ← in standard form

with a = 1, b = - 1, c = 14

b² - 4ac

= (- 1)² - (4 × 1 × 14) = 1 - 56 = - 55

Since b² - 4ac < 0 then roots are not real

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