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

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

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Answer 1 · 2018-03-20T08:21:59

$x = + \sqrt{\frac{57}{16}} - \frac{3}{4} = 1.1374$ $x=+sqrt(57/16)-3/4 = 1.1374$

or

$x = - \sqrt{\frac{57}{16}} - \frac{3}{4} = - 2.6374$ $x=-sqrt(57/16)-3/4 = -2.6374$

Explanation:

$x^{2} + \frac{3}{2} x = 3$ $x^2+3/2x=3$

$\Rightarrow x^{2} + \frac{3}{2} x - 3 = 0$ $=> x^2+3/2x-3=0$

$\Rightarrow {(x + \frac{3}{4})}^{2} - {(\frac{3}{4})}^{2} - 3 = 0$ $=> (x+3/4)^2-(3/4)^2-3=0$

$\Rightarrow {(x + \frac{3}{4})}^{2} - (\frac{9}{16}) - 3 = 0$ $=> (x+3/4)^2-(9/16)-3=0$

$\Rightarrow {(x + \frac{3}{4})}^{2} - (\frac{9}{16}) - (\frac{48}{16}) = 0$ $=> (x+3/4)^2-(9/16)-(48/16)=0$

$\Rightarrow {(x + \frac{3}{4})}^{2} - (\frac{57}{16}) = 0$ $=> (x+3/4)^2-(57/16)=0$

$\Rightarrow {(x + \frac{3}{4})}^{2} = \frac{57}{16}$ $=> (x+3/4)^2=57/16$

$\Rightarrow x + \frac{3}{4} = \pm \sqrt{\frac{57}{16}}$ $=> x+3/4=+-sqrt(57/16)$

$\Rightarrow x = \pm \sqrt{\frac{57}{16}} - \frac{3}{4}$ $=> x=+-sqrt(57/16)-3/4$

Therefore, x is either

$x = + \sqrt{\frac{57}{16}} - \frac{3}{4} = 1.1374$ $x=+sqrt(57/16)-3/4 = 1.1374$

$x = - \sqrt{\frac{57}{16}} - \frac{3}{4} = - 2.6374$ $x=-sqrt(57/16)-3/4 = -2.6374$

Answer 2 · 2018-03-20T08:27:47

$x = \frac{- 3 \pm \sqrt{57}}{4}$ $x=(-3+-sqrt57)/4$

Explanation:

$x^{2} + \frac{3}{2} x = 3$ $x^2+3/2 x =3$

Add ${(\frac{3}{4})}^{2}$ $(3/4)^2$ both sides.

$\Rightarrow x^{2} + \frac{3}{2} x + {(\frac{3}{4})}^{2} = 3 + {(\frac{3}{4})}^{2}$ $=> x^2+3/2x+(3/4)^2 = 3+(3/4)^2$

$\Rightarrow {(x)}^{2} + 2 \times x \times \frac{3}{4} + {(\frac{3}{4})}^{2} = 3 + \frac{9}{16}$ $=> (x)^2 + 2xx x xx3/4 + (3/4)^2 = 3+9/16$

$\Rightarrow {(x + \frac{3}{4})}^{2} = \frac{57}{16}$ $=> (x+3/4)^2 = 57/16$

$\Rightarrow x + \frac{3}{4} = \frac{\pm \sqrt{57}}{4}$ $=> x+3/4=(+-sqrt57)/4$

$\Rightarrow x = \frac{\pm \sqrt{57}}{4} - \frac{3}{4}$ $=> x=(+-sqrt57)/4 - 3/4$

$\Rightarrow x = \frac{- 3 \pm \sqrt{57}}{4}$ $=> x=(-3+-sqrt57)/4$

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2 Answers

Explanation:

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