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daser333 [38]
3 years ago
11

If using the method of completing the square to solve the quadratic equation x^2-10x-13=0, which number would have to be added t

o "complete the square"?
Mathematics
1 answer:
Maru [420]3 years ago
6 0

Answer: The solution to the problem is based on the solutions

from the subproblems.

x = {8.464101615, 1.535898385}

Step-by-step explanation:  

x^2-10x+13=0

Simplifying

x2 + -10x + 13 = 0

Reorder the terms:

13 + -10x + x2 = 0

Solving

13 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.

13 + -10x + -13 + x2 = 0 + -13

Reorder the terms:

13 + -13 + -10x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0

0 + -10x + x2 = 0 + -13

-10x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13

-10x + x2 = -13

The x term is -10x.  Take half its coefficient (-5).

Square it (25) and add it to both sides.

Add '25' to each side of the equation.

-10x + 25 + x2 = -13 + 25

Reorder the terms:

25 + -10x + x2 = -13 + 25

Combine like terms: -13 + 25 = 12

25 + -10x + x2 = 12

Factor a perfect square on the left side:

(x + -5)(x + -5) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting  

(x + -5) equal to 3.464101615 and -3.464101615.

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250 pounds of Robusta beans.
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Which of the following ordered pairs is a solution of X+1/2y=1
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-2+1/2 (6) I'd 1 so A is correct
6 0
3 years ago
Twin brothers, Billy and Bobby, can mow their grandparent’s lawn together in 63 minutes. Billy could mow the lawn by himself in
Pepsi [2]

Answer:

<h2>140 minutes</h2>

Step-by-step explanation:

this problem focuses on the combined work rate

both can finish the work under 63 minute

let bobby mow the lawn in x minute

Billy will then mow the lawn in x-25 minutes

Let the completed job = 1 (a mowed lawn)

we can now apply the combined work formula for the two boys as

\frac{63}{x}+\frac{63}{x-25}=1

multiplying through by x(x-25 )we have

63(x-25)+63x= x(x-25)

open bracket we have

63x-1575+63x= x^2-25x

rearranging and collecting like terms we have

0=x^2-25x-63x-63x+1575 \\\\0=x^2-151x+1575 \\\\x^2-151x+1575=0

we can now use the quadractic formula

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

 

a= 1

b= -151

c= 1575

x=\frac{-(-151)\frac{+}{} \sqrt{151^2-4*1*1575} }{2*1}

x=\frac{-(-151)\frac{+}{} \sqrt{22801-6300} }{2} \\\\x=\frac{-(-151)\frac{+}{} \sqrt{16501} }{2} \\\\x=\frac{-(-151)\frac{+}{} 128.45}{2} \\\\

x=\frac{-(-151)+128.45}{2} \\\\\x=\frac{279.45}{2} \\\\x=139.72 \\\\\\x=\frac{-(-151)-128.45}{2}\\\\x=\frac{151-128.45}{2}\\\\x=\frac{22.55}{2}\\\\x=11.27

the first answer x= 139.72 approximately 140 minutes mins is correct for  Bobby's time

let us check

\frac{63}{140}+\frac{63}{140-25}=1\\\\\\0.45+\frac{63}{115} =1\\\\0.45+0.5478=1\\0.997 =1

we can see that the solution approximates to 1

8 0
3 years ago
Mandy cut 34 1⁄3 feet of string to use for the tail of a kite. However, she realized that the tail was too long and cut off 6 3⁄
andrezito [222]
34 1/3- 6 3/5= 416/15

8 0
3 years ago
2 determinar el valor del patrimonio con los siguientes datos Caja= 10,000 Bancos= 13,500 Cuentas por pagar= 8,000 Documentos po
Softa [21]

Answer:

PN= $17,800

Step-by-step explanation:

<u>La formula general para calcular el activo de una empresa es la siguiente:</u>

<u></u>

A= PN + P

El activo es igual al patrimonio neto y el pasivo.

Debemos intercambiar los términos:

PN= A - P

Activo:

Caja= 10,000

Bancos= 13,500

Equipos de computación= 2,400

Documentos por cobrar= 5,100

Pasivo:

Cuentas por pagar= 8,000

Documentos por pagar= 4,000

Intereses por pagar= 1,200

PN= 31,000 - 13,200

PN= $17,800

7 0
3 years ago
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