Question

Use the quadratic formula to find both solutions to the quadratic equation given below x^2+6x=27

Answer 1

option (d) and (f) is correct.

The solution of given quadratic equation is 3 and -9.

Explanation:

Given quadratic equation
`x^2+6x=27`

We have to solve the given quadratic equation using quadratic formula.

Consider
`x^2+6x=27` , we can rewrite it as
`x^2+6x-27=0`

For the general quadratic equation
`ax^2+bx+c=0` the quadratic formula is given as
`x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)`

Here a = 1 , b= 6 and c = -27

Substitute, we get,

`x_(1,\:2)=(-6\pm √(6^2-4\cdot \:1\left(-27\right)))/(2\cdot \:1)`

Solving further , we get,

`x_(1,2)=(-6\pm√(6^2+4\cdot \:1\cdot \:27))/(2\cdot \:1)`

`x_(1,2)=(-6\pm√(144))/(2\cdot \:1)`

We know
`√(144)=12`, we get,

`x_(1,2)=(-6\pm 12)/(2\cdot \:1)`

`x_(1)=(-6+12)/(2)` and
`x_(2)=(-6-12)/(2)`

Solving we get,

`x_(1)=(6)/(2)` and
`x_(2)=(-18)/(2)`

`x_(1)=3` and
`x_(2)=-9`

Thus, the solution of given quadratic equation is 3 and -9.

Thus, option (d) and (f) is correct.

Answer 2

x=3 or x=−9

Explanation:

Step 1: Subtract 27 from both sides.

x2+6x−27=27−27

x2+6x−27=0

Step 2: Factor left side of equation.

(x−3)(x+9)=0

Step 3: Set factors equal to 0.

x−3=0 or x+9=0

x=3 or x=−9

Answer:

x=3 or x=−9