(x-4)^2 + 5^2 = 13^2 quadratic equation
Answers
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(x-4)^2+5^2-(13^2)=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(((x - 4)2) + (52)) - 132 = 0
Step 2 :
Equation at the end of step 2 :
(((x - 4)2) + 52) - 132 = 0
Step 3 :
Trying to factor by splitting the middle term
3.1 Factoring x2-8x-128
The first term is, x2 its coefficient is 1 .
The middle term is, -8x its coefficient is -8 .
The last term, "the constant", is -128
Step-1 : Multiply the coefficient of the first term by the constant 1 • -128 = -128
Step-2 : Find two factors of -128 whose sum equals the coefficient of the middle term, which is -8 .
-128 + 1 = -127
-64 + 2 = -62
-32 + 4 = -28
-16 + 8 = -8 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -16 and 8
x2 - 16x + 8x - 128
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-16)
Add up the last 2 terms, pulling out common factors :
8 • (x-16)
Step-5 : Add up the four terms of step 4 :
(x+8) • (x-16)
Which is the desired factorization
Equation at the end of step 3 :
(x + 8) • (x - 16) = 0
Step 4 :
Theory - Roots of a product :
4.1 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 :
4.2 Solve : x+8 = 0
Subtract 8 from both sides of the equation :
x = -8
Solving a Single Variable Equation :
4.3 Solve : x-16 = 0
Add 16 to both sides of the equation :
x = 16
Answer:x= 16 or x= -8
Step-by-step explanation:
(x-4)^2 + 5^2 = 13^2
(x-4)^2 = 13^2 - 5^2
using, a^2-b^2= (a+b) (a-b), on RHS.
(x-4)^2= (13+5) (13-5)
(x-4)^2= 18×8
(x-4)^2= 144=12×12=12^2, So
x-4= +12, or x-4 = -12
x= 16 or x= -8