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What is the first step in solving the equation x2 – 16/25 = 0?

Keith_Richards [23]

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x^2-(16/25)=0

Step by step solution :Step 1 : 16 Simplify —— 25 Equation at the end of step 1 : 16 (x2) - —— = 0 25 Step 2 :Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 25 as the denominator :

x2 x2 • 25 x2 = —— = ——————— 1 25

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x2 • 25 - (16) 25x2 - 16 —————————————— = ————————— 25 25 Trying to factor as a Difference of Squares :

2.3 Factoring: 25x2 - 16

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =
 A2 - AB + BA - B2 =
 A2 - AB + AB - B2 =
 A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 25 is the square of 5
Check : 16 is the square of 4
Check : x2 is the square of x1 

Factorization is : (5x + 4) • (5x - 4)

Equation at the end of step 2 : (5x + 4) • (5x - 4) ——————————————————— = 0 25 Step 3 :When a fraction equals zero : 3.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

(5x+4)•(5x-4) ————————————— • 25 = 0 • 25 25

Now, on the left hand side, the 25 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
(5x+4) • (5x-4) = 0

Theory - Roots of a product :

3.2 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

3.3 Solve : 5x+4 = 0

Subtract 4 from both sides of the equation :
 5x = -4
Divide both sides of the equation by 5:
 x = -4/5 = -0.800

Solving a Single Variable Equation :

3.4 Solve : 5x-4 = 0

Add 4 to both sides of the equation :
 5x = 4
Divide both sides of the equation by 5:
 x = 4/5 = 0.800

x = 4/5 = 0.800
 x = -4/5 = -0.800

3 0

3 years ago

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fred had a tray of brownies for his birthday. he ate 1/6 of the brownies by himself and his family ate 1/3 of the brownies how m

snow_lady [41]

We want to know how many brownmies did Fred and his family eat together.

We will call to the total of the brownies by 1. On this case, after Fred ate 1/3 of the brownies, he will have:

$1-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}$

This means that he has left 2/3 of the brownies. After his family ate 1/6 of the brownies:

$\frac{2}{3}-\frac{1}{6}=\frac{4}{6}-\frac{1}{6}=\frac{3}{6}=\frac{1}{2}$

This means they will have left 1/2 of the tray of brownies, and that they ate half of it.

6 0

11 months ago

Pls guys help me with this i will give u more points!

gtnhenbr [62]

$3x - 4y = - 6 \\ - 2x + y = 1$

The Ordered pair of solution will be (x,y)=(2,3)

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<h3>Steps below⤵️</h3>

Solve the second equation for y
Substitute the given value of y into the first equation
Solve the first equation for x
Substitute the given value of x into the second equation
Solve the equation for y
The possible solution of the system is the ordered pair (x,y)
And we are done solving!!~

5 0

2 years ago

This is an easy question. Whoever answered this is worthy of getting these points. A florist sells a dozen roses for $35.40. she

Savatey [412]

Answer:

Answer: The equation is

The cost of 18 roses is 53.10.

Step-by-step explanation:

Given:

A florist sells a dozen roses for 35.40. She sells individual roses for the same unit price.

Now, to find the cost of 18 roses and write an equation to represent the relationship between the number of roses, x, and the total cost of the roses, y.

1 dozen = 12.

Now, to get the cost of 18 roses we use unitary method:

If 12 roses cost = 35.40.

So, 1 roses cost = 2.95.

Thus, 18 roses cost = 53.10.

Therefore, the cost of 18 roses = 53.10.

Now, to write an equation the relationship between the number of roses and the total cost of the roses:

Cost of per rose = 2.95.

As, given in question:

Number of roses =

Total cost of the roses =

Total cost of the roses = Cost of per rose × Number of roses.

So, the equation is:

Therefore, the equation is And the cost of 18 roses is 53.10.

Step-by-step explanation:

6 0

3 years ago

Three consecutive natural numbers have a sum of 36. What is the greatest number?

Eduardwww [97]

It's 12 because if you divide 36 by 3 (consecutive) it equals 12

8 0

3 years ago

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