5-2x2=-15
Two solutions were found :
x = ± √10 = ± 3.1623
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
5-2*x^2-(-15)=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(5 - 2x2) - -15 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
20 - 2x2 = -2 • (x2 - 10)
Trying to factor as a Difference of Squares :
3.2 Factoring: x2 - 10
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 : 10 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step 3 :
-2 • (x2 - 10) = 0
Step 4 :
Equations which are never true :
4.1 Solve : -2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
4.2 Solve : x2-10 = 0
Add 10 to both sides of the equation :
x2 = 10
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 10
The equation has two real solutions
These solutions are x = ± √10 = ± 3.1623
Two solutions were found :
x = ± √10 = ± 3.1623
