Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Rewrite the equation by completing the square. {:[4x^(2)-12 x+9=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $4x^{2}-12x+9=0$ $\newline$ $(x+\square)^{2}=\square$

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}-12x+9=0

\newline

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

Identifying Coefficients: We start by identifying the coefficient of $x^2$ , which is $4$ , and the coefficient of $x$ , which is $-12$ . The constant term is $9$ . The equation is already set to equal zero, which is the first step in completing the square.
Factoring Out Coefficient: To complete the square, we need to factor out the coefficient of $x^2$ from the first two terms. In this case, we factor out $4$ from $4x^2$ and $-12x$ . $\newline$ $4(x^2 - 3x) + 9 = 0$
Completing the Square: Next, we find the value that completes the square for the expression $x^2 - 3x$ . To do this, we take half of the coefficient of $x$ , which is $-\frac{3}{2}$ , and square it, resulting in $\left(\frac{3}{2}\right)^2 = \frac{9}{4}$ .
Adding and Subtracting Value: We add and subtract this value inside the parentheses to maintain the equality. Since we factored out a $4$ at the beginning, we need to add and subtract $4$ times the value that completes the square. $\newline$ $4(x^2 - 3x + \frac{9}{4} - \frac{9}{4}) + 9 = 0$
Simplifying the Equation: Now we simplify the equation by combining like terms inside the parentheses and adjusting the constant term outside. $4(x^2 - 3x + \frac{9}{4}) - 4(\frac{9}{4}) + 9 = 0$
Simplifying Constants: Simplify the constants outside the parentheses. $\newline$ $4(x^2 - 3x + \frac{9}{4}) - 9 + 9 = 0$ $\newline$ $4(x^2 - 3x + \frac{9}{4}) = 0$
Writing as Perfect Square Trinomial: The expression inside the parentheses is now a perfect square trinomial, which can be written as $(x - \frac{3}{2})^2$ . $\newline$ $4(x - \frac{3}{2})^2 = 0$
Rewriting the Equation: Finally, we rewrite the equation in the completed square form. $(x - \frac{3}{2})^2 = 0$

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