x^2+17x-18=0 equation formula
Answers
Step-by-step explanation:
x^2+17x-18=0
x^2+18x-x-18=0
x(x+18) -1(x+18) = 0
(x+18)(x-1) = 0
Answer:-x=1
x=−18
Factoring x2+17x-18
The first term is, x2 its coefficient is 1 .
The middle term is, +17x its coefficient is 17 .
The last term, "the constant", is -18
Step-1 : Multiply the coefficient of the first term by the constant 1 • -18 = -18
Step-2 : Find two factors of -18 whose sum equals the coefficient of the middle term, which is 17 .
-18 + 1 = -17 -9 + 2 = -7 -6 + 3 = -3 -3 + 6 = 3 -2 + 9 = 7 -1 + 18 = 17 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and 18
x2 - 1x + 18x - 18
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-1)
Add up the last 2 terms, pulling out common factors :
18 • (x-1)
Step-5 : Add up the four terms of step 4 :
(x+18) • (x-1)
Which is the desired factorization
Equation at the end of step1:
(x + 18) • (x - 1) = 0
STEP2:Theory - Roots of a product
2.1 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:
2.2 Solve : x+18 = 0
Subtract 18 from both sides of the equation :
x = -18
Solving a Single Variable Equation:
2.3 Solve : x-1 = 0
Add 1 to both sides of the equation :
x = 1