Which of the following correctly completes the the square for the equation below? x^2+18x=0

2 answers:

Nookie1986 [14]3 years ago

4 0

X² +18x = 0

To complete the square we are going to use formula a² +2ab +b² = (a+b)²

x² +2*9*x = 0
x² +2*9x+9² = 9²
(x+9)² = 9²
√(x+9)² = +/-√9²
x+9 = 9, or x+9 = -9
x=0, or x= - 18

The equation could be solved different way
x² +18x = 0
x(x+18) = 0
x=0 or x+18=0
x=0 or x=-18

My name is Ann [436]3 years ago

3 0

We know that a perfect square has the form
(x+y)^2 = x^2+2xy+y^2
If we substitute the numbers in the given equation, we have
(x+y)^2 = x^2+2xy+y^2 = x^2+2x(9) + y^2
By comparison of the coefficients of the term xy, we have y=9, hence we need y^2=9^2=81 to complete the square.

The completed square would be
(x+9)^2-81=0 (which expands back to x^2+18x=0)

However, if the objective is to solve the equation, I would solve it by factoring, i.e.
x^2+18x=0 => x(x+18)=0 => x=0 or x=-18

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The area of a rectangular garden if 6045 ft2. If the length of the garden is 93 feet, what is its width?

AnnyKZ [126]

Answer:

65 ft

Step-by-step explanation:

The area of a rectangle is

A = lw

6045 = 93*w

Divide each side by 93

6045/93 = 93w/93

65 =w

4 0

2 years ago

Read 2 more answers

Select the two values of x that are roots of this equation

Jet001 [13]

<h2>Hello!</h2>

The answers are:

B. $\frac{-3-\sqrt{29}}{2}$

C. $\frac{-3+\sqrt{29}}{2}$

We can use the quadratic equation to find the two values of x that are roots of the given equation. We must remember that most of the quadratic equations have two roots, however, we could find quadratic equations with just one root or even with no roots, at least in the real numbers.

Quadratic equation:

$\frac{-b+-\sqrt{b^{2}-4ac} }{2a}$

So,

From the given equation we have:

$a=1\\b=3\\c=-5$

Substituting it into the quadratic equation to find the roots, we have:

$\frac{-b+-\sqrt{b^{2}-4ac} }{2a}=\frac{-3+-\sqrt{3^{2}-4*1*-5} }{2*1}\\\\\frac{-3+-\sqrt{3^{2}-4*1*-5} }{2*1}=\frac{-3+-\sqrt{9+20} }{2}\\\\\frac{-3+-\sqrt{29}}{2}$