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4 years ago

Solve for equation √-5p=√24-p

Mathematics

1 answer:

blsea [12.9K]4 years ago

8 0

Answer:

Step-by-step explanation:

25,219,829 solved | 850 online

p2-5p-24=0

Two solutions were found :

p = 8

p = -3

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "p2" was replaced by "p^2".

Step by step solution :

Step 1 :

Trying to factor by splitting the middle term

1.1 Factoring p2-5p-24

The first term is, p2 its coefficient is 1 .

The middle term is, -5p its coefficient is -5 .

The last term, "the constant", is -24

Step-1 : Multiply the coefficient of the first term by the constant 1 • -24 = -24

Step-2 : Find two factors of -24 whose sum equals the coefficient of the middle term, which is -5 .

-24 + 1 = -23

-12 + 2 = -10

-8 + 3 = -5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 3

p2 - 8p + 3p - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

p • (p-8)

Add up the last 2 terms, pulling out common factors :

3 • (p-8)

Step-5 : Add up the four terms of step 4 :

(p+3) • (p-8)

Which is the desired factorization

Equation at the end of step 1 :

(p + 3) • (p - 8) = 0

Step 2 :

Theory - Roots of a product :

2.1 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 :

2.2 Solve : p+3 = 0

Subtract 3 from both sides of the equation :

p = -3

Solving a Single Variable Equation :

2.3 Solve : p-8 = 0

Add 8 to both sides of the equation :

p = 8

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3 years ago

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Answer:

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Step-by-step explanation:

We can write an exponential function to model the situation. The standard exponential function is:

$f(t)=a(r)^t$

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Alternatively, we can use the standard exponential growth/decay function modeled by:

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