# Solve by completing the square;round to the nearest hundredth if necessary.

x^2-3x=4

Thanks so much.

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1. x^2 - 3 x = 4

x^2 -3 x +(3/2)^2 = 4 + 9/4

(x-1.5)^2 = (1/4)(16 + 9)

(x-1.5)^2 = (1/4)(25) = 25/4

x-3/2 = +/- 5/2

x = 3/2 +/- 5/2

x = 4 or x = -1

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2. x ^ 2 - 3 x = 4

The x-term coefficient = − 3

The half of the x-term coefficient = − 3 / 2

After squaring you have ( − 3 / 2 ) ^ 2= 9 / 4

x ^ 2 - 3 x = 4

Add 9 / 4 to both sides

x ^ 2 - 3 x + 9 / 4 = 4 + 9 / 4

x ^ 2 - 3 x + 9 / 4 = 16 / 4 + 9 / 4

x ^ 2 - 3 x + 9 / 4 = 25 / 4

Write the perfect square on the left side:

( x - 3 / 2 ) ^ 2 = 25 / 4

Take the square root of both sides:

x - 3 / 2 = sqroot ( 25 / 4 )

x - 3 / 2 = ± 5 / 2 Add 3 / 2 to both sides

x - 3 / 2 + 3 / 2 = ± 5 / 2 + 3 / 2

x = ± 5 / 2 + 3 / 2

x1 = 5 / 2 + 3 / 2 = 8 / 2 = 4

x2 = - 5 / 2 + 3 / 2 = - 2 / 2 = - 1

The solutions are :

x = - 1 and x = 4

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Remark:

x ^ 2 - 3 x + 9 / 4 = ( x - 3 / 2 ) ^ 2 becouse:

( x - 3 / 2 ) ^ 2 =

x ^ 2 - 2 * x * 3 / 2 + ( 3 / 2 ) ^ 2 =

x ^ 2 - x * 3 + 9 / 4 =

x ^ 2 - 3 x + 9 / 4
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3. 1.C
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3.B
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5.B

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4. answers is correct!!! 100%

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