Solve the quadratic equation x^2 - 3(x + 3) = 0; Give your answer… - Vidyadip

Question

Solve the quadratic equation $x^2 - 3(x + 3) = 0$; Give your answer correct two significant figures

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Answer

$x^2-3(x+3)=0$
$\Rightarrow x^2-3 x-9=0$
Comparing with $a x^2+b y+c$ we get
$\therefore x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} $
$ \Rightarrow x=\frac{-(-3) \pm \sqrt{(-3)^2-4(1)(-9)}}{2(1)} $.
$ \Rightarrow x=\frac{3 \pm \sqrt{9+36}}{2} $
$ \Rightarrow x=\frac{3 \pm \sqrt{45}}{2}$
$ \Rightarrow x=\frac{3 \pm \sqrt{9 \times 5}}{2}$
$ \Rightarrow x=\frac{3 \pm 3 \sqrt{5}}{2}$
$ \Rightarrow x=\frac{3+3 \sqrt{5}}{2} \text { or } x=\frac{3-3 \sqrt{5}}{2}$
$\Rightarrow x=\frac{3+3 \times 2.236}{2} \text { or } x=\frac{3-3 \times 2.236}{2}$
$\Rightarrow x=\frac{3+6.708}{2} \text { or } x=\frac{3-6.708}{2}$
$ \Rightarrow x=\frac{9.708}{2} \text { or } x=\frac{-3.708}{2}$
$ \Rightarrow x =4.85 \text { or } x =-1.85$
$ \Rightarrow x =4.9 \text { or } x =-1.9$

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