Bot GPT 4-o mini To determine if a given value is a solution to the quadratic equation \(x^2 + 20x = 69\), we can first rewrite the equation in standard form:
\[ x^2 + 20x - 69 = 0 \]
Next, we will assess whether each provided value, let's say \(x = a\), satisfies the equation by substituting it in:
\[ a^2 + 20a - 69 = 0 \]
For demonstration, I will verify if some common values could be solutions. If you have specific values to test, please provide them, and I will adjust accordingly.
Here’s how you would test some arbitrary values to determine if they satisfy the equation:
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For example, test \(x = -30\): \[ (-30)^2 + 20(-30) - 69 = 900 - 600 - 69 = 231 \quad (\text{Not a solution}) \]
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Next, test \(x = -10\): \[ (-10)^2 + 20(-10) - 69 = 100 - 200 - 69 = -169 \quad (\text{Not a solution}) \]
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Next, test \(x = -3\): \[ (-3)^2 + 20(-3) - 69 = 9 - 60 - 69 = -120 \quad (\text{Not a solution}) \]
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Finally, test \(x = -1\): \[ (-1)^2 + 20(-1) - 69 = 1 - 20 - 69 = -88 \quad (\text{Not a solution}) \]
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Now let's test \(x = 3\): \[ (3)^2 + 20(3) - 69 = 9 + 60 - 69 = 0 \quad (\text{This is a solution}) \]
Identifying the correct solution: After testing all relevant values, only \(x = 3\) satisfies the equation.
So, if this matches one of your test values, you can fill in the blank with \(3\).
The answer would then be:
Only \(x = \boxed{3}\) is in the solution set.
If you have other specific values to test or further instructions, please provide them, and I'll help you through it!
1 answer