Question
Solve for x using the quadratic formula. Write your answer correct to two significant figures: $(x – 1)^2 – 3x + 4 = 0.$
✓
Answer
$
\begin{aligned}
& (x-1)^2-3 x+4=0 \\
& x^2-2 x+1-3 x+4=0 \\
& x^2-5 x+5=0
\end{aligned}
$
Here $a=1, b=-5$ and $c=5$
$
\begin{aligned}
& x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\
& x=\frac{-(5) \pm \sqrt{(-5)^2-4(1)(5)}}{2} \\
& =\frac{5 \pm \sqrt{25-20}}{2} \\
& =\frac{5 \pm \sqrt{5}}{2} \\
& =\frac{5+2.236}{2} \text { or } \frac{5-2.236}{2} \\
& =\frac{7.236}{2} \text { or } \frac{2.764}{2} \\
& =3.618 \text { or } 1.382 \\
& \therefore x=3.618 \approx 3.6 \text { or } 1.382 \approx 1.4
\end{aligned}
$
\begin{aligned}
& (x-1)^2-3 x+4=0 \\
& x^2-2 x+1-3 x+4=0 \\
& x^2-5 x+5=0
\end{aligned}
$
Here $a=1, b=-5$ and $c=5$
$
\begin{aligned}
& x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\
& x=\frac{-(5) \pm \sqrt{(-5)^2-4(1)(5)}}{2} \\
& =\frac{5 \pm \sqrt{25-20}}{2} \\
& =\frac{5 \pm \sqrt{5}}{2} \\
& =\frac{5+2.236}{2} \text { or } \frac{5-2.236}{2} \\
& =\frac{7.236}{2} \text { or } \frac{2.764}{2} \\
& =3.618 \text { or } 1.382 \\
& \therefore x=3.618 \approx 3.6 \text { or } 1.382 \approx 1.4
\end{aligned}
$
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