How do you solve by completing the square for $x^2+ 3/2x = 3$ ?

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How do you solve by completing the square for $x^2+ 3/2x = 3$ ?

2 Answers

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Answer 1 · 2018-03-20T08:21:59

$x=+sqrt(57/16)-3/4 = 1.1374$

or

$x=-sqrt(57/16)-3/4 = -2.6374$

Explanation:

$x^2+3/2x=3$

$=> x^2+3/2x-3=0$

$=> (x+3/4)^2-(3/4)^2-3=0$

$=> (x+3/4)^2-(9/16)-3=0$

$=> (x+3/4)^2-(9/16)-(48/16)=0$

$=> (x+3/4)^2-(57/16)=0$

$=> (x+3/4)^2=57/16$

$=> x+3/4=+-sqrt(57/16)$

$=> x=+-sqrt(57/16)-3/4$

Therefore, x is either

$x=+sqrt(57/16)-3/4 = 1.1374$

$x=-sqrt(57/16)-3/4 = -2.6374$

Answer 2 · 2018-03-20T08:27:47

$x=(-3+-sqrt57)/4$

Explanation:

$x^2+3/2 x =3$

Add $(3/4)^2$ both sides.

$=> x^2+3/2x+(3/4)^2 = 3+(3/4)^2$

$=> (x)^2 + 2xx x xx3/4 + (3/4)^2 = 3+9/16$

$=> (x+3/4)^2 = 57/16$

$=> x+3/4=(+-sqrt57)/4$

$=> x=(+-sqrt57)/4 - 3/4$

$=> x=(-3+-sqrt57)/4$

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How do you solve by completing the square for $x^2+ 3/2x = 3$ ?

2 Answers

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