Question

Solve x2 − 3x = −8.

x equals quantity of 3 plus or minus I square root of 29 all over 2


x equals quantity of 3 plus or minus I square root of 23 all over 2


x equals quantity of negative 3 plus or minus I square root of 29 all over 2


x equals quantity of negative 3 plus or minus I square root of 23 all over 2

Answer 1

x equals 3 plus or minus i square root of 23 all over 2

Explanation:

I got it right on the test.

Answer 2

we have

`x^(2) -3x=-8`

Complete the square. Remember to balance the equation by adding the same constants to each side

`x^(2) -3x+1.5^(2)=-8+1.5^(2)`

`x^(2) -3x+1.5^(2)=-5.75`

Rewrite as perfect squares

`(x-1.5)^(2)=-5.75`

Square Root both sides

`x-1.5=(+/-)√(-5.75)`

Remember that

`√(-1)=i`

`√(5.75)= \sqrt{(23)/(4)}=(√(23))/(2)`

Substitute

`x-1.5=(+/-)i(√(23))/(2)`

`x=1.5(+/-)i(√(23))/(2)`

`x=(3/2)(+/-)i(√(23))/(2)`

`x=(3/2)+i(√(23))/(2)=(3+i√(23))/(2)`

`x=(3/2)-i(√(23))/(2)=(3-i√(23))/(2)`

therefore

the answer is

x equals quantity of 3 plus or minus I square root of 23 all over 2