25|x|=x^2+144
answer step by step
Answers
Answer:
_/107
Step-by-step explanation:
251-144=x^2
107=x^2
x=_/107
Answer:
25|x|=x^2+144
Step-by-step explanation:
25(x2-144)+12(x2-25)=x2
Two solutions were found :
x = ±√ 108.333 = ± 10.40833
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
25*(x^2-144)+12*(x^2-25)-(x^2)=0
Step by step solution :
Step 1 :
Trying to factor as a Difference of Squares :
1.1 Factoring: x2-25
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 : 25 is the square of 5
Check : x2 is the square of x1
Factorization is : (x + 5) • (x - 5)
Equation at the end of step 1 :
((25•((x2)-144))+12•(x+5)•(x-5))-x2 = 0
Step 2 :
Trying to factor as a Difference of Squares :
2.1 Factoring: x2-144
Check : 144 is the square of 12
Check : x2 is the square of x1
Factorization is : (x + 12) • (x - 12)
Equation at the end of step 2 :
(25•(x+12)•(x-12)+12•(x+5)•(x-5))-x2 = 0
Step 3 :
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
36x2 - 3900 = 12 • (3x2 - 325)
Trying to factor as a Difference of Squares :
4.2 Factoring: 3x2 - 325
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 4 :
12 • (3x2 - 325) = 0
Step 5 :
Equations which are never true :
5.1 Solve : 12 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
5.2 Solve : 3x2-325 = 0
Add 325 to both sides of the equation :
3x2 = 325
Divide both sides of the equation by 3:
x2 = 325/3 = 108.333
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 325/3
The equation has two real solutions
These solutions are x = ±√ 108.333 = ± 10.40833
Two solutions were found :
x = ±√ 108.333 = ± 10.40833