Question

Solve the following quadratic equation and show all the working:


x² − 7x + 3 = 0

Answer 1

Answer:

Solution

=

7

±

3

7

√

2

Step-by-step explanation:

Use the quadratic formula

=

−

±

2

−

4

√

2

x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}

x=2a−b±b2−4ac

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

2

−

7

+

3

=

0

x^{2}-7x+3=0

x2−7x+3=0

=

1

a={\color{#c92786}{1}}

a=1

=

−

7

b={\color{#e8710a}{-7}}

b=−7

=

3

c={\color{#129eaf}{3}}

c=3

=

−

(

−

7

)

±

(

−

7

)

2

−

4

⋅

1

⋅

3

√

2

⋅

1

Answer 2

Answer:

${x}^{2} - 7x + 3 = 0 \\ \\ x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} \\ x = \frac{ - ( - 7)± \sqrt{ {( - 7)}^{2} - 4(1)(3)} }{2 \times 1} \\ x= \frac{7± \sqrt{49 - 12} }{2} \\ x = \frac{7± \sqrt{37} }{2} \\ \boxed{ x = \underline{ \underline{ \frac{7 + \sqrt{37} }{2} }} \: \: \: or \: \: \: x = \underline{ \underline{ \frac{7 - \sqrt{37} }{2} }}}$