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Solve the following quadratic equation for all values of xx in simplest form.9, left bracket, x, squared, minus, 8, right bracket, minus, 1, equals, minus, 99(x 2 −8)−1=−9

Question

Solve the following quadratic equation for all values of xx in simplest form.9, left bracket, x, squared, minus, 8, right bracket, minus, 1, equals, minus, 99(x 2 −8)−1=−9

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Solution

The equation you provided is: 9(x^2 - 8) - 1 = -9. Let's solve it step by step:

Step 1: Distribute the 9 to both terms in the parentheses: 9x^2 - 72 - 1 = -9

Step 2: Combine like terms: 9x^2 - 73 = -9

Step 3: Add 73 to both sides to isolate the x^2 term: 9x^2 = 64

Step 4: Divide both sides by 9: x^2 = 64/9

Step 5: Take the square root of both sides. Remember, when you take the square root of a number, there is a positive and a negative solution: x = ± √(64/9)

Step 6: Simplify the square root: x = ± 8/3

So, the solutions to the equation are x = 8/3 and x = -8/3.

This problem has been solved

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