solved quadratic equation 5x square+13x+8=0
Answers
Step-by-step explanation:
5x2-13x+8=0
Two solutions were found :
x = 1
x = 8/5 = 1.600
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(5x2 - 13x) + 8 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 5x2-13x+8
The first term is, 5x2 its coefficient is 5 .
The middle term is, -13x its coefficient is -13 .
The last term, "the constant", is +8
Step-1 : Multiply the coefficient of the first term by the constant 5 • 8 = 40
Step-2 : Find two factors of 40 whose sum equals the coefficient of the middle term, which is -13 .
-40 + -1 = -41
-20 + -2 = -22
-10 + -4 = -14
-8 + -5 = -13 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and -5
5x2 - 8x - 5x - 8
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (5x-8)
Add up the last 2 terms, pulling out common factors :
1 • (5x-8)
Step-5 : Add up the four terms of step 4 :
(x-1) • (5x-8)
Which is the desired factorization
Equation at the end of step 2 :
(5x - 8) • (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 : 5x-8 = 0
Add 8 to both sides of the equation :
5x = 8
Divide both sides of the equation by 5:
x = 8/5 = 1.600
Solving a Single Variable Equation :
3.3 Solve : x-1 = 0
Add 1 to both sides of the equation :
x = 1
Supplement : Solving Quadratic Equation Directly
Solving 5x2-13x+8 = 0 directly
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