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A quadratic equation is show 4(x+7)^(2)=11 Solve the equation and create

User Anga
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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
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