14 Subtract the expressions.
A. -5x -(-3x²+ 24)
Answers
-5x+3x²+24
minus × minus = plus
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Answer:
STEP
1
:
Equation at the end of step 1
3x2 - 24 = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
3x2 - 24 = 3 • (x2 - 8)
Trying to factor as a Difference of Squares:
3.2 Factoring: x2 - 8
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 : 8 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step
3
:
3 • (x2 - 8) = 0
STEP
4
:
Equations which are never true
4.1 Solve : 3 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
4.2 Solve : x2-8 = 0
Add 8 to both sides of the equation :
x2 = 8
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 8
Can √ 8 be simplified ?
Yes! The prime factorization of 8 is
2•2•2
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 8 = √ 2•2•2 =
± 2 • √ 2
The equation has two real solutions
These solutions are x = 2 • ± √2 = ± 2.8284
Step-by-step explanation: