Factorise : 7x^2-15=0
Answers
Answer:
STEP
1
:
Equation at the end of step 1
15 - 7x2 = 0
STEP
2
:
Trying to factor as a Difference of Squares:
2.1 Factoring: 15-7x2
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 : 15 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Equation at the end of step
2
:
15 - 7x2 = 0
STEP
3
:
Solving a Single Variable Equation:
3.1 Solve : -7x2+15 = 0
Subtract 15 from both sides of the equation :
-7x2 = -15
Multiply both sides of the equation by (-1) : 7x2 = 15
Divide both sides of the equation by 7:
x2 = 15/7 = 2.143
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 15/7
The equation has two real solutions
These solutions are x = ±√ 2.143 = ± 1.46385
Step-by-step explanation:
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