Question

2. Consider the equation x2 + 8x = 10.

(a) Show how to solve the equation by completing the square.
(b) Show how to solve the equation by using the quadratic formula. Round solutions to the nearest tenth if needed.

Answer 1

x=1.1 or x=-9.1

Step-by-step explanation

`{x}^(2) + 8x = 10`

Ad the square of half the coefficient of x to both sides:

`{x}^(2) + 8x + {4}^(2) = 10 + {4}^(2)`

`{x}^(2) + 8x + 16= 10 + 16`

The left hand side is now a perfect square.

`{(x + 4)}^(2) = 26`

Take square root

`x + 4= \pm √(26)`

`x = - 4 \pm √(26)`

x=1.1 or x=-9.1

Using the quadratic formula, we need to rewrite the given equation to get;

`{x}^(2) + 8x - 10 = 0`

where a=1, b=8 and c=-10

The solution is given by:

`x = \frac{ - b \pm \: \sqrt{ {b}^(2) - 4ac } }{2a}`

We substitute the values into the formula to get;

`x = \frac{ - 8\pm \: \sqrt{ {8}^(2) - 4(1)( - 10) } }{2(1)}`

`x = ( - 8\pm \: √( 104 ) )/(2)`

`x = ( - 8\pm \: 2√( 26 ) )/(2)`

`x = - 4\pm \: √( 26 )`

x=1.1 or x=-9.1

to the nearest tenth.