Write quadratic equation in the standard
form 5y+4= y²
Answers
Answer:
y2-5y-4
Step-by-step explanation:
Hope this helps
Changes made to your input should not affect the solution:
(1): "y2" was replaced by "y^2".
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y^2-(5*y-4)=0
Step by step solution :
STEP
1
:
Trying to factor by splitting the middle term
1.1 Factoring y2-5y+4
The first term is, y2 its coefficient is 1 .
The middle term is, -5y its coefficient is -5 .
The last term, "the constant", is +4
Step-1 : Multiply the coefficient of the first term by the constant 1 • 4 = 4
Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is -5 .
-4 + -1 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and -1
y2 - 4y - 1y - 4
Step-4 : Add up the first 2 terms, pulling out like factors :
y • (y-4)
Add up the last 2 terms, pulling out common factors :
1 • (y-4)
Step-5 : Add up the four terms of step 4 :
(y-1) • (y-4)
Which is the desired factorization
Equation at the end of step
1
:
(y - 1) • (y - 4) = 0
STEP
2
:
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 : y-1 = 0
Add 1 to both sides of the equation :
y = 1
Solving a Single Variable Equation:
2.3 Solve : y-4 = 0
Add 4 to both sides of the equation :
y = 4
Supplement : Solving Quadratic Equation Directly
Solving y2-5y+4 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
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