solve quadratic equation: m²+12m+20=0
Answers
Step-by-step explanation:
m=−2
m=−10
See steps
Step by Step Solution:
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Reformatting the input :
Changes made to your input should not affect the solution:
(1): "m2" was replaced by "m^2".
Step by step solution :
STEP
1
:
Trying to factor by splitting the middle term
1.1 Factoring m2+12m+20
The first term is, m2 its coefficient is 1 .
The middle term is, +12m its coefficient is 12 .
The last term, "the constant", is +20
Step-1 : Multiply the coefficient of the first term by the constant 1 • 20 = 20
Step-2 : Find two factors of 20 whose sum equals the coefficient of the middle term, which is 12 .
-20 + -1 = -21
-10 + -2 = -12
-5 + -4 = -9
-4 + -5 = -9
-2 + -10 = -12
-1 + -20 = -21
1 + 20 = 21
2 + 10 = 12 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 2 and 10
m2 + 2m + 10m + 20
Step-4 : Add up the first 2 terms, pulling out like factors :
m • (m+2)
Add up the last 2 terms, pulling out common factors :
10 • (m+2)
Step-5 : Add up the four terms of step 4 :
(m+10) • (m+2)
Which is the desired factorization
Equation at the end of step
1
:
(m + 10) • (m + 2) = 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 : m+10 = 0
Subtract 10 from both sides of the equation :
m = -10
Solving a Single Variable Equation:
2.3 Solve : m+2 = 0
Subtract 2 from both sides of the equation :
m = -2
Supplement : Solving Quadratic Equation Directly
Solving m2+12m+20 = 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
Step-by-step explanation:
a= m2
b= 12m
c = 20
so multiply a × c
then write the factors of the answers
that is
m2 × 20 = 20m2
its factors are 10× 2
so
we can write
m2 + 10m + 2m + 20 = 0
m ( m + 10 ) + 2 ( m + 10 ) = 0
m+ 2 , m+ 10
so
m+ 2 = 0
m= -2
and m + 10 = 0
m = -10
that's it
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