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ziro4ka [17]
3 years ago
7

Find the value of c that completes the square for x2−15x+c

Mathematics
1 answer:
meriva3 years ago
5 0

Answer:

The value of <em>c</em> is \frac{225}{4}.

Step-by-step explanation:

The perfect square of the difference between two numbers is:

(x-y)^{2}=x^{2}-2xy+y^{2}

The expression provided is:

x^{2}-15x+c

The expression is a perfect square of the difference between two numbers.

One of the number is <em>x</em> and the other is √<em>c</em>.

Use the above relation to compute the value of <em>c</em> as follows:

x^{2}-15x+c=(x-\sqrt{c})^{2}\\\\x^{2}-15x+c=x^{2}-2\cdot x\cdot\sqrt{c}+c\\\\15x=2\cdot x\cdot\sqrt{c}\\\\15=2\cdot\sqrt{c}\\\\\sqrt{c}=\frac{15}{2}\\\\c=[\frac{15}{2}]^{2}\\\\c=\frac{225}{4}

Thus, the value of <em>c</em> is \frac{225}{4}.

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