Question

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

Answer 1

Answer:

option (d) and (f) is correct.

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

Step-by-step 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 $x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

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

Substitute, we get,

$x_{1,\:2}=\frac{-6\pm \sqrt{6^2-4\cdot \:1\left(-27\right)}}{2\cdot \:1}$

Solving further , we get,

$x_{1,2}=\frac{-6\pm\sqrt{6^2+4\cdot \:1\cdot \:27}}{2\cdot \:1}$

$x_{1,2}=\frac{-6\pm\sqrt{144}}{2\cdot \:1}$

We know $\sqrt{144}=12$, we get,

$x_{1,2}=\frac{-6\pm 12}{2\cdot \:1}$

$x_{1}=\frac{-6+12}{2}$ and $x_{2}=\frac{-6-12}{2}$

Solving we get,

$x_{1}=\frac{6}{2}$ and $x_{2}=\frac{-18}{2}$

$x_{1}=3$ and $x_{2}=-9$

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

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

 

Answer 2

Answer:

x=3 or x=−9

Step-by-step 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