Question

Let ​ x^2+13x=−3 ​ .

Answer 1

Answer:  The required values are $\dfrac{169}{4}~~\textup{and}~~\dfrac{157}{4}.$

Step-by-step explanation:  The given quadratic equation is

$x^2+13x=-3~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to find the values that make an equivalent number sentence after completing the square.

COMPLETING THE SQUARE :  Its a method of making one side of a quadratic equation a perfect square, so that the equation can be solved easily by taking the square root on both the sides of the equation.

From equation (i), we have

$x^2+13x=-3\\\\\Rightarrow x^2+2\times x\times \dfrac{13}{2}+\left(\dfrac{13}{2}\right)^2=\left(\dfrac{13}{2}\right)^2-3\\\\\\\Rightarrow \left(x+\dfrac{13}{2}\right)^2=\dfrac{169}{4}-3\\\\\\\Rightarrow \left(x+\dfrac{13}{2}\right)^2=\dfrac{157}{4}.$

So, the complete statement is

$x^2+13x+\dfrac{169}{4}=\dfrac{157}{4}.$

Thus, the required values are $\dfrac{169}{4}~~\textup{and}~~\dfrac{157}{4}.$

Answer 2

Answer:out of these what is the correct answer

Step-by-step explanation: