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3 years ago

(x+3)²(65)=x(6)Solve using quadric formula

Mathematics

2 answers:

Angelina_Jolie [31]3 years ago

6 0

Step 1: Simplify both sides of the equation.

65x²+390x+585=6x

Step 2: Subtract 6x from both sides.

65x²+390x+585−6x=6x−6x
65x²+384x+585=0

For this equation: a=65, b=384, c=585

65x²+384x+585=0

Step 3: Use quadratic formula with a=65, b=384, c=585

x=−b±√b2−4ac/2a
x=−(384)±√(384)2−4(65)(585)/
2(65)
x=−384±√−4644/130

Therefore, There are no real solutions.

lakkis [162]3 years ago

5 0

Answer:

Use the commutative property to reorder the terms ==> 65(x + 3)^2 = x × 6 ==> 6(x + 3)^2 = 6x

Use (a + b)^2 = a^2 + 2ab + b^2 to expand the expression ==> 65(x^2 + 6x + 9) = 6x

Distribute 65 through the parentheses ==> 65^2 + 390x + 585 = 6x

Move the variable to the left-hand side and change its sign ==> 6x^2 + 390x + 585 - 6x = 0

its sign ==> 6x^2 + 390x + 585 - 6x = 0Collect like terms ==> 65x^2 + 384x + 585 = 0

its sign ==> 6x^2 + 390x + 585 - 6x = 0Collect like terms ==> 65x^2 + 384x + 585 = 0Solve the quadratic equation ==> (that part and onward is in the attachment)

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Let us take two same decimal numbers $2.14$ , $7.25$ and a fraction $\frac{5}{20}$

Now, according to the Associated property of Addition:

For any three numbers $a$ , $b$ and $c$

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So, for $2.14$ , $7.25$ and $\frac{5}{20}$

The Left hand side:

$a + (b+c)$

$2.14 + (7.25 + \frac{5}{20}) = 2.14 + (\frac{725}{100} + \frac{5 \times 5}{20\times 5})$

$= 2.14 + (\frac{725}{100} + \frac{25 }{100})$

$= 2.14 + (\frac{750}{100} )$

$= \frac{214}{100} + \frac{750}{100}$

$= \frac{964}{100}$

$=9.64$

The Right hand side:

$(a + b )+c$

$(2.14 + 7.25 )+ \frac{5}{20}= ( 9.39 ) + \frac{5 }{20}$

$= 9.39 + \frac{5 \times 5 }{20 \times 5}$

$= 9.39 + \frac{25}{100}$

$= 9.39 + 0.25$

$= 9.64$

Thus,

$(2.14 + (7.25 + \frac{5}{20} )= (2.14 + 7.25 )+ \frac{5}{20}$

Therefore, $2.14+\frac{5}{20} = \frac{5}{20} + 2.14$

Hence, Associative Property of Addition is satisfied.

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(x+3)²(65)=x(6)Solve using quadric formula​

(x+3)²(65)=x(6)Solve using quadric formula