Solve equation 4x2 - 45x + 81 = 0.
Answers
Step-by-step explanation:
4x2-45x+81=0
Two solutions were found :
x = 9/4 = 2.250
x = 9
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(22x2 - 45x) + 81 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 4x2-45x+81
The first term is, 4x2 its coefficient is 4 .
The middle term is, -45x its coefficient is -45 .
The last term, "the constant", is +81
Step-1 : Multiply the coefficient of the first term by the constant 4 • 81 = 324
Step-2 : Find two factors of 324 whose sum equals the coefficient of the middle term, which is -45 .
-324 + -1 = -325
-162 + -2 = -164
-108 + -3 = -111
-81 + -4 = -85
-54 + -6 = -60
-36 + -9 = -45 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -36 and -9
4x2 - 36x - 9x - 81
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (x-9)
Add up the last 2 terms, pulling out common factors :
9 • (x-9)
Step-5 : Add up the four terms of step 4 :
(4x-9) • (x-9)
Which is the desired factorization
Equation at the end of step 2 :
(x - 9) • (4x - 9) = 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 : x-9 = 0
Add 9 to both sides of the equation :
x = 9
Solving a Single Variable Equation :
3.3 Solve : 4x-9 = 0
Add 9 to both sides of the equation :
4x = 9
Divide both sides of the equation by 4:
x = 9/4 = 2.250
Answer:
x = -9/4 or 9
Step-by-step explanation:
4x² - 45x + 81 = 0 ... (i)
4 * 81 = 324
Factors of 324 are (1, 324), (2, 162), (3,108) , (4, 81), (6, 54), (9, 36) , (12, 27) , (18 , 18)
-36 - 9 = -45
Rewriting equation (i),
4x² - 36x - 9x + 81 = 0
⇒ 4x (x -9) + 9 (x - 9) = 0
⇒ (4x + 9) (x - 9) = 0
⇒ 4x + 9 = 0 or x - 9 = 0
⇒ 4x = -9 or x = 9
⇒ x = -9/4 or 9