Question

If using the method of completing the square to solve the quadratic equation x^2+15x+34=0x
2
+15x+34=0, which number would have to be added to "complete the square"?

Answer 1

Answer:

56.25

Step-by-step explanation:

\text{Number to add: }\frac{15}{2}=7.5\rightarrow (7.5)^2=\color{blue}{56.25}

Number to add:  

2

15

​

=7.5→(7.5)

2

=56.25

Half of b then square

x^2+15x\color{blue}{+56.25}=

x

2

+15x+56.25=

\,\,-34\color{blue}{+56.25}

−34+56.25

Add to both sides

(x+7.5)^2=

(x+7.5)

2

=

\,\,22.25

22.25

\text{Square now completed.}

Square now completed.

\text{Number added: }\mathbf{56.25}\text{ or }\mathbf{\frac{225}{4}}

Number added: 56.25 or  

4

225

​

Answer 2

In order to solve the quadratic equation x²+15x+34=0 the number 225/4 would have to be added to "complete the square"

What is a quadratic equation ?

Any equation of the form $\rm ax^2+bx+c=0$ where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

$\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}$

We have a quadratic equation:

x² + 15x + 34=0

(x—15/2)² + 34 – 225/4 = 0

The number is 225/4

Thus, in order to solve the quadratic equation x²+15x+34=0 the number 225/4 would have to be added to "complete the square"

Learn more about quadratic equations here:

brainly.com/question/2263981

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