Question

4 square minus 100 is equal to zero

Answer 1

Answer:

Step-by-step explanation:

4 square is 16

So, 100-16= 84

Answer 2

Step-by-step explanation:

4x2-100=0

Two solutions were found :

x = 5

x = -5

Step by step solution :

Step 1 :

Equation at the end of step 1 :

22x2 - 100 = 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

4x2 - 100 = 4 • (x2 - 25)

Trying to factor as a Difference of Squares :

3.2 Factoring: x2 - 25

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 : x2 is the square of x1

Factorization is : (x + 5) • (x - 5)

Equation at the end of step 3 :

4 • (x + 5) • (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.

Equations which are never true :

4.2 Solve : 4 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.3 Solve : x+5 = 0

Subtract 5 from both sides of the equation :

x = -5

Solving a Single Variable Equation :

4.4 Solve : x-5 = 0

Add 5 to both sides of the equation :

x = 5