Solve the quadratic equation 2x^2– 7x + 5 = 0 by
completing the square method.
Answers
Answer:
2.5
Step-by-step explanation:
2x2-7x+5=0
Two solutions were found :
x = 1
x = 5/2 = 2.500
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(2x2 - 7x) + 5 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 2x2-7x+5
The first term is, 2x2 its coefficient is 2 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is +5
Step-1 : Multiply the coefficient of the first term by the constant 2 • 5 = 10
Step-2 : Find two factors of 10 whose sum equals the coefficient of the middle term, which is -7 .
-10 + -1 = -11
-5 + -2 = -7 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -2
2x2 - 5x - 2x - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-5)
Add up the last 2 terms, pulling out common factors :
1 • (2x-5)
Step-5 : Add up the four terms of step 4 :
(x-1) • (2x-5)
Which is the desired factorization
Equation at the end of step 2 :
(2x - 5) • (x - 1) = 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 : 2x-5 = 0
Add 5 to both sides of the equation :
2x = 5
Divide both sides of the equation by 2:
x = 5/2 = 2.500