Math, asked by afnad2005, 10 months ago

5x2 + 5x +1 split the middle term
I want the best answers please

Answers

Answered by Khushi2558
1

Two solutions were found :

x = -5

x = 1/5 = 0.200

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((0 - 5x2) - 24x) + 5 = 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

-5x2 - 24x + 5 = -1 • (5x2 + 24x - 5)

Trying to factor by splitting the middle term

3.2 Factoring 5x2 + 24x - 5

The first term is, 5x2 its coefficient is 5 .

The middle term is, +24x its coefficient is 24 .

The last term, "the constant", is -5

Step-1 : Multiply the coefficient of the first term by the constant 5 • -5 = -25

Step-2 : Find two factors of -25 whose sum equals the coefficient of the middle term, which is 24 .

-25 + 1 = -24

-5 + 5 = 0

-1 + 25 = 24 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and 25

5x2 - 1x + 25x - 5

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

x • (5x-1)

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

5 • (5x-1)

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

(x+5) • (5x-1)

Which is the desired factorization

Equation at the end of step 3 :

(1 - 5x) • (x + 5) = 0

Step 4 :

Theory - Roots of a product :

4.1 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 :

4.2 Solve : -5x+1 = 0

Subtract 1 from both sides of the equation :

-5x = -1

Multiply both sides of the equation by (-1) : 5x = 1

Divide both sides of the equation by 5:

x = 1/5 = 0.200

Solving a Single Variable Equation :

4.3 Solve : x+5 = 0

Subtract 5 from both sides of the equation :

x = -5

Supplement : Solving Quadratic Equation Directly

Solving 5x2+24x-5 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

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