3 times a number is 54 less than the square of that number. Find the negative solution.
Question
3 times a number is 54 less than the square of that number. Find the negative solution.
Solution
Sure, let's solve this step by step:
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Let's denote the number as x. According to the problem, we can write the equation as: 3x = x^2 - 54.
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To solve for x, we need to rearrange the equation to a standard quadratic form ax^2 + bx + c = 0. So, we get: x^2 - 3x - 54 = 0.
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Now, we can factor this quadratic equation. The factors of -54 that add up to -3 are -9 and 6. So, we can write the equation as: (x - 9)(x + 6) = 0.
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Setting each factor equal to zero gives the solutions x = 9 and x = -6.
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Since the problem asks for the negative solution, the answer is x = -6.
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