Question

Square root of 3x^2-50​

Answer 1

Two solutions were found :

x = ±√ 16.667 = ± 4.08248

Step by step solution :

Step 1 :

Equation at the end of step 1 :

3x2 - 50 = 0

Step 2 :

Trying to factor as a Difference of Squares :

2.1 Factoring: 3x2-50

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 : 3 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Equation at the end of step 2 :

3x2 - 50 = 0

Step 3 :

Solving a Single Variable Equation :

3.1 Solve : 3x2-50 = 0

Add 50 to both sides of the equation :

3x2 = 50

Divide both sides of the equation by 3:

x2 = 50/3 = 16.667

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 50/3

The equation has two real solutions

These solutions are x = ±√ 16.667 = ± 4.08248

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