Quadratic equation 36x²-169=0
Answers
Answer:
6^2x^2=169
6x=root169
6x=13
x=13/6
Answer:
Step 1 :
Equation at the end of step 1 :
(22•32x2) - 169 = 0
Step 2 :
Trying to factor as a Difference of Squares :
2.1 Factoring: 36x2-169
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 : 36 is the square of 6
Check : 169 is the square of 13
Check : x2 is the square of x1
Factorization is : (6x + 13) • (6x - 13)
Equation at the end of step 2 :
(6x + 13) • (6x - 13) = 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.
Solving a Single Variable Equation :
3.2 Solve : 6x+13 = 0
Subtract 13 from both sides of the equation :
6x = -13
Divide both sides of the equation by 6:
x = -13/6 = -2.167
Solving a Single Variable Equation :
3.3 Solve : 6x-13 = 0
Add 13 to both sides of the equation :
6x = 13
Divide both sides of the equation by 6:
x = 13/6 = 2.167
Two solutions were found :
x = 13/6 = 2.167
x = -13/6 = -2.167
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(22•32x2) - 169 = 0
Step 2 :
Trying to factor as a Difference of Squares :
2.1 Factoring: 36x2-169
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 : 36 is the square of 6
Check : 169 is the square of 13
Check : x2 is the square of x1
Factorization is : (6x + 13) • (6x - 13)
Equation at the end of step 2 :
(6x + 13) • (6x - 13) = 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.
Solving a Single Variable Equation :
3.2 Solve : 6x+13 = 0
Subtract 13 from both sides of the equation :
6x = -13
Divide both sides of the equation by 6:
x = -13/6 = -2.167
Solving a Single Variable Equation :
3.3 Solve : 6x-13 = 0
Add 13 to both sides of the equation :
6x = 13
Divide both sides of the equation by 6:
x = 13/6 = 2.167
Two solutions were found :
x = 13/6 = 2.167
x = -13/6 = -2.167
Hope it will help you