Rewrite the equation by completing the square:
2x²-3x-5=0

(x-¾)² = 49/16

Step-by-step explanation:

0 = 2x² - 3x - 5

2x² - 3x = 5

Divide by the leading coefficient

x²-(3/2)x = 5/2

Complete the square

 coefficient of the x term: 3/2

 divide coefficient in half: ¾

 square it: (¾)²

 add (¾)² to both sides to complete the square and keep the equation balanced:

x²-(3/2)x + (¾)² = 5/2 + (¾)²

(x-¾)² = 49/16

If you need to solve for x:

x-¾ = ±√(49/16) = ±7/4

x = 5/2, -1

step-by-step explanation:

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