3.13: Completing the square for a maximum value

0606/21/O/N/23 — Question 1 · 9 marks

(a)
Write 19−12x−3x219 - 12x - 3x^{2} in the form a(x+b)2+ca(x + b)^{2} + c where aa, bb and cc are integers.
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(b)
Hence find the maximum value of 19−12x−3x219 - 12x - 3x^{2} and the value of xx at which this maximum occurs.
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(c)
Use your answer to part (a) to solve the equation 19−12u−3u2=019 - 12u - 3u^{2} = 0.
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