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
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.
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