Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Rewrite the equation by completing the square. {:[x^(2)+11 x+24=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2+11x+24=0$ $\newline$ $(x+\square)^2=\square$

View step-by-step help

View step-by-step help

Solve a quadratic equation by completing the square

Full solution

Q. Rewrite the equation by completing the square.

\newline

x^2+11x+24=0

\newline

(x+\square)^2=\square

Move constant term: $x^2 + 11x + 24 = 0$ $\newline$ First, we need to move the constant term to the right side of the equation to prepare for completing the square. $\newline$ $x^2 + 11x = -24$
Complete the square: $x^2 + 11x = -24$ $\newline$ To complete the square, we need to add the square of half the coefficient of $x$ to both sides of the equation. The coefficient of $x$ is $11$ , so half of $11$ is $5.5$ , and the square of $5.5$ is $30.25$ . $\newline$ $x^2 + 11x + 30.25 = -24 + 30.25$
Simplify right side: $x^2 + 11x + 30.25 = -24 + 30.25$ $\newline$ Now, we simplify the right side of the equation by adding $-24$ and $30.25$ . $\newline$ $x^2 + 11x + 30.25 = 6.25$
Write as perfect square trinomial: $x^2 + 11x + 30.25 = 6.25$ $\newline$ The left side of the equation is now a perfect square trinomial, and can be written as $(x + 5.5)^2$ . $\newline$ $(x + 5.5)^2 = 6.25$

More problems from Solve a quadratic equation by completing the square

Question

v

\newline

v^2+8v+12=0

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

v=

Posted 5 days ago

Question

u

\newline

u^2 = 9

\newline

Write your answers as integers or as proper or improper fractions in simplest form.

\newline

u =

u =

Posted 3 months ago

Question

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

\newline

k^2 - 20k + \_\_\_\_\_

Posted 2 months ago

Question

Solve by completing the square.

\newline

u^2 - 24u - 23 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

`u` = ________ or `u` =______

Posted 2 months ago

Question

Find the discriminant.

\newline

2q^2 - 9q + 8 = 0

\newline

Posted 2 months ago

Question

Solve the system of equations.

\newline

y = 22x - 38

\newline

y = x^2 + 11x - 14

\newline

Write the coordinates in exact form. Simplify all fractions and radicals.

\newline

(\_,\_)

\newline

(\_,\_)

Posted 2 months ago

Question

a

\newline

(a + 5)(a + 1) = 0

\newline

Write your answers as integers or as proper or improper fractions in simplest form.

\newline

a =

a =

Posted 2 months ago

Question

p=x^{2}-7

. Which equation is equivalent to

(x^{2}-7)^{2}-4x^{2}+28=5

p

1

\newline

p^{2}-4p+23=0

\newline

p^{2}+4p-5=0

\newline

p^{2}-4p-5=0

\newline

p^{2}+4p+23=0

Posted 2 months ago

Question

m=2x+3

. Which equation is equivalent to

(2x+3)^{2}-14x-21=-6

m

1

\newline

m^{2}+7m+6=0

\newline

m^{2}-7m-15=0

\newline

m^{2}-7m+6=0

\newline

m^{2}+7m-15=0

Posted 2 months ago

Question

m=x^{2}+3

. Which equation is equivalent to

(x^{2}+3)^{2}+7x^{2}+21=-10

m

1

\newline

m^{2}-7m+31=0

\newline

m^{2}+7m+31=0

\newline

m^{2}-7m+10=0

\newline

m^{2}+7m+10=0

Posted 3 months ago