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

Use the quadratic formula to find both solutions to the quadratic equation given below-example-1

2 Answers

6 votes

Answer:

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.

User OptimusCrime
by
8.5k points
2 votes

Answer:

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

User Ayohaych
by
7.2k points

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