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What are the solutions to m2 – 9 = 0?

User Cmather
by
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1 Answer

1 vote

Answer:

m2-9=0

Explanation:

Two solutions were found :

m = 3

m = -3

Step by step solution :

Step 1 :

Trying to factor as a Difference of Squares :

1.1 Factoring: m2-9

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 : 9 is the square of 3

Check : m2 is the square of m1

Factorization is : (m + 3) • (m - 3)

Equation at the end of step 1 :

(m + 3) • (m - 3) = 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 : m+3 = 0

Subtract 3 from both sides of the equation :

m = -3

Solving a Single Variable Equation :

2.3 Solve : m-3 = 0

Add 3 to both sides of the equation :

m = 3

User Twaddington
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