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Which of the following are solutions to the equation

Which of the following are solutions to the equation-example-1
User Greggles
by
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1 Answer

1 vote

Hello! Your answer would be A and B, 5 and 4.

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First, move all values to one side. This will give us the quadratic equation we are looking for to solve (and make it much easier).

x² - 3x + 27 = 6x + 7

x² - 9x + 20 = 0

Now, factor the equation. Essentially, turn it into the form of (x + a)(x + b), where a + b must equal -9 in this case (the coefficient of x) and a * b must equal, in this case, 20.

The numbers which when added equal -9 and multiplied equal 20 are negative 5 and negative 4.

Substitute these into (x + a)(x + b).

(x - 5)(x - 4) = 0

Now, recall that anything multiplied by 0 is equal to 0. This can be applied in this scenario because we are looking to make either (x - 5) or (x - 4) equal to 0, as that would set the entire left side equal to 0, and make our equation correct.

To do this, x would either have to equal 5 or 4. This is because 5 - 5 = 0, and 4 - 4 = 0.

Therefore, your two solutions to the equation are 5 and 4.

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If you would like confirmation:

5² - 3*5 + 27 = 6*5 + 7

25 - 15 + 27 = 30 + 7

37 = 37

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4² - 3*4 + 27 = 6*4 + 7

16 - 12 + 27 = 24 + 7

31 = 31

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Hope this helps!

User Kamran Kausar
by
5.7k points