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 c 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 x and the other is √c.

Use the above relation to compute the value of c 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 c is $\frac{225}{4}$ .

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