Question

Let ​ x² + 15x = 49 .​ What values make an equivalent number sentence after completing the square? Enter your answers in the boxes.
x² + 15x + ​= ​ [ ]

Answer 1

Answer:

$x^2+15x+\boxed{\dfrac{225}{4}}=\boxed{\dfrac{421}{4}}$

$x^2+15x+\boxed{56.25}=\boxed{105.25}$

Step-by-step explanation:

General form of a quadratic equation: $ax^2+bx+c$

When completing the square, first add the number that is the square of half of $b$.

Given equation:  $x^2+15x=49$

Therefore, $b=15$

$\implies \left(\dfrac{b}{2}\right)^2=\left(\dfrac{15}{2}\right)^2=\dfrac{225}{4}$

So we need to add 225/4 to both sides of the equation:

$\implies x^2+15x+\dfrac{225}{4}=49+\dfrac{225}{4}$

$\implies x^2+15x+\boxed{\dfrac{225}{4}}=\boxed{\dfrac{421}{4}}$

In decimal form:

$\implies x^2+15x+\boxed{56.25}=\boxed{105.25}$

To finish completing the square,

factor the left side of the equation:

$\implies \left(x+\dfrac{15}{2}\right)^2=\dfrac{421}{4}$

Finally, subtract 421/4 from both sides:

$\implies \left(x+\dfrac{15}{2}\right)^2-\dfrac{421}{4}=0$

In decimal form:

$\implies (x+7.5)^2-105.25=0$

Answer 2

Answer:

Step-by-step explanation:

15/2 = 7.5 and (7.5)^2 = 56.25  so

x^2 + 15x + 56.25 = 49 + 56.25

x^2 + 15x + 56.25 = 105.25.