Question

Let ​ x² + 15x = 49 .​

Answer 1

Answer:  $x^2+15x+56.25=105.25$

Step-by-step explanation:

Given equation: $x^2+15x=49$

The coefficient of x = 15

For completing the square we need to add square of half of coefficient of x on both the sides of the given equation.

Square of half of coefficient of x=$(\frac{15}{2})^2$ =56.25

Now, add $(\frac{15}{2})^2$ on both sides of the given equation we get

$x^2+15x +(\frac{15}{2})^2=49+(\frac{15}{2})^2\\\\\Rightarrow\ x^2+15x+\frac{225}{4}=49+\frac{225}{4}\\\\\Rightarrow\ x^2+15x+56.25=49+56.25\\\Rightarrow\ x^2+15x+56.25=105.25$

Answer 2

Since the numerical coefficient of the first term is only 1, we determine the number that needs to be added to both sides of the equation by squaring half of the second term. That is,
                                   third term = (15/2)² = 56.25
Thus, the missing terms are,
                          x² + 15x + 56.25 = 49 + 56.25
equal to,
                            x² + 15x + 56.25 = 105.25