Answer: TWO SOLUTIONS:
x = 3
x = -3
Explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*x^2-1-(17)=0
Step by step solution : STEP 1:
Equation at the end of step 1
(2x2 - 1) - 17 = 0
STEP 2 :
Pulling out like terms
3.1 Pull out like factors :
2x2 - 18 = 2 • (x2 - 9)
Trying to factor as a Difference of Squares:
3.2 Factoring: x2 - 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 : x2 is the square of x1
Factorization is : (x + 3) • (x - 3)
Equation at the end of step 2:
2 • (x + 3) • (x - 3) = 0
STEP 3:
Theory - Roots of a product
3.1 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:
3.2 Solve : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
4.3 Solve : x+3 = 0
Subtract 3 from both sides of the equation :
x = -3
Solving a Single Variable Equation:
4.4 Solve : x-3 = 0
Add 3 to both sides of the equation :
x = 3
Two solutions were found :
x = 3
x = -3