Answer:
[tex]x = 1 \ + \sqrt{-19}\ or\ x = 1 \ - \sqrt{-19}[/tex]
Step-by-step explanation:
Given
[tex]x^2 + 20 = 2x[/tex]
Required
Solve using quadratic formula
We start by representing the above equation property
[tex]x^2 + 20 = 2x[/tex]
Subtract 2x from both sides
[tex]x^2 + 20 - 2x= 2x - 2x[/tex]
[tex]x^2 + 20 - 2x= 0[/tex]
[tex]x^2 -2x + 20 = 0[/tex]
Given a quadratic equation of the form [tex]ax^2 +bx + c = 0[/tex]
The quadratic formula is as follows;
[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
Where a = 1, b = -2 and c = 20
[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]x = \frac{-(-2) \± \sqrt{(-2)^2 - 4*1*20}}{2 * 1}[/tex]
[tex]x = \frac{2 \± \sqrt{4 - 80}}{2}[/tex]
[tex]x = \frac{2 \± \sqrt{-76}}{2}[/tex]
Factorize -76
[tex]x = \frac{2 \± \sqrt{-19 * 4}}{2}[/tex]
Split the square root
[tex]x = \frac{2 \± \sqrt{-19} *\sqrt{4}}{2}[/tex]
Square root of 4 is 2
[tex]x = \frac{2 \± \sqrt{-19} * 2}{2}[/tex]
[tex]x = \frac{2 \± 2\sqrt{-19}}{2}[/tex]
Split Fraction
[tex]x = \frac{2}{2} \± \frac{2\sqrt{-19}}{2}[/tex]
[tex]x = 1 \ + \sqrt{-19}\ or\ x = 1 \ - \sqrt{-19}[/tex]
The expression can not be further simplified;
Hence, [tex]x = 1 \ + \sqrt{-19}\ or\ x = 1 \ - \sqrt{-19}[/tex]
