Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Rewrite the equation by completing the square. {:[4x^(2)+20 x+25=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $4x^{2}+20x+25=0$ $\newline$ $(x+\square)^{2}=\square$

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

4x^{2}+20x+25=0

\newline

(x+\square)^{2}=\square

Factor out coefficient of x^ $2$ : We are given the quadratic equation $4x^2 + 20x + 25 = 0$ . To complete the square, we want to express the equation in the form $(x + \square)^2 = \square$ . First, we need to factor out the coefficient of $x^2$ from the first two terms on the left side of the equation. $\newline$ $4(x^2 + 5x) + 25 = 0$
Find number to fill the square: Next, we need to find a number to fill the square ( $\square$ ) that makes $x^2 + 5x$ into a perfect square trinomial. We take half of the coefficient of $x$ , which is $\frac{5}{2}$ , and square it to get $\left(\frac{5}{2}\right)^2 = \frac{25}{4}$ . $\newline$ $4\left(x^2 + 5x + \frac{25}{4}\right) + 25 - 4 \times \frac{25}{4} = 0$
Add and subtract to balance equation: We add and subtract $\frac{25}{4}$ inside the parentheses to keep the equation balanced. We then multiply the subtracted $\frac{25}{4}$ by $4$ to subtract it from the outside of the parentheses. $\newline$ $4(x^2 + 5x + \frac{25}{4}) - 25 = 0$
Write as a squared binomial: Now we have a perfect square trinomial inside the parentheses, and we can write it as a squared binomial. $4(x + \frac{5}{2})^2 - 25 = 0$
Isolate the squared binomial: Finally, we add $25$ to both sides to isolate the squared binomial. $\newline$ $4(x + \frac{5}{2})^2 = 25$
Divide both sides to solve: To complete the square, we divide both sides by $4$ to solve for the squared binomial. $\newline$ $(x + \frac{5}{2})^2 = \frac{25}{4}$

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 1 month 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 2 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 1 month 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 2 months ago