218k views
1 vote
A quadratic equation is show 4(x+7)^(2)=11 Solve the equation and create

User Anga
by
7.4k points

1 Answer

4 votes

Firstly, we want to convert the equation into a more standard form by getting rid of the constant (4) that is multiplying the square. We do this by dividing both sides of the equation by 4:

4(x + 7)² = 11
(x + 7)² = 11 / 4

Now, it is time to take the square root of both sides of the equation. The square root of a squared term cancels the square, and remember that when you take the square root of a number you get two solutions: positive and negative.

So (x + 7) equals to sqrt(11 / 4) and -sqrt(11 / 4), respectively.

To solve for x, simply subtract 7 from both sides:

x = sqrt(11 / 4) - 7

This gives us the solution corresponding to the positive square root. In the case of the negative square root, the equation is:

x = -sqrt(11 / 4) - 7

Therefore, we have two solutions to the original equation:

The value of x1, when taking the positive root, is -5.3416876048223.
The value of x2, when taking the negative root, is -8.658312395177699.

So the solution set for the given equation is x1 = -5.3416876048223 and x2 = -8.658312395177699.

User UVic
by
7.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories