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

Question

asked Jul 22, 2023 85.6k views

2 Answers

Tim Lindsey · Answer 1 · 2023-07-27T07:11:21+0000

Answer:

$x^2+15x+\boxed{(225)/(4)}=\boxed{(421)/(4)}$

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

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
.

Given equation:
x^2+15x=49

Therefore,
b=15

$\implies \left((b)/(2)\right)^2=\left((15)/(2)\right)^2=(225)/(4)$

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

$\implies x^2+15x+(225)/(4)=49+(225)/(4)$

$\implies x^2+15x+\boxed{(225)/(4)}=\boxed{(421)/(4)}$

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:

$\implies \left(x+(15)/(2)\right)^2=(421)/(4)$

Finally, subtract 421/4 from both sides:

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

In decimal form:

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