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Alenkinab [10]
2 years ago
15

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

Mathematics
2 answers:
Dmitriy789 [7]2 years ago
8 0

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.

 

docker41 [41]2 years ago
7 0

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

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