x²+5x-15000=0 solve the quadratic equation
Answers
Answer:
The first term is, x2 its coefficient is 1 .
The middle term is, +5x its coefficient is 5 .
The last term, "the constant", is -15000
Step-1 : Multiply the coefficient of the first term by the constant 1 • -15000 = -15000
Step-2 : Find two factors of -15000 whose sum equals the coefficient of the middle term, which is 5 .
-15000 + 1 = -14999
-7500 + 2 = -7498
-5000 + 3 = -4997
-3750 + 4 = -3746
-3000 + 5 = -2995
-2500 + 6 = -2494
-1875 + 8 = -1867
-1500 + 10 = -1490
-1250 + 12 = -1238
-1000 + 15 = -985
-750 + 20 = -730
-625 + 24 = -601
-600 + 25 = -575
-500 + 30 = -470
-375 + 40 = -335
-300 + 50 = -250
-250 + 60 = -190
-200 + 75 = -125
-150 + 100 = -50
-125 + 120 = -5
-120 + 125 = 5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -120 and 125
x2 - 120x + 125x - 15000
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-120)
Add up the last 2 terms, pulling out common factors :
125 • (x-120)
Step-5 : Add up the four terms of step 4 :
(x+125) • (x-120)
Which is the desired factorization
Equation at the end of step
2
:
(-x - 125) • (x - 120) = 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-125 = 0
Add 125 to both sides of the equation :
-x = 125
Multiply both sides of the equation by (-1) : x = -125
Solving a Single Variable Equation:
3.3 Solve : x-120 = 0
Add 120 to both sides of the equation :
x = 120
Supplement : Solving Quadratic Equation Directly
Solving x2+5x-15000 = 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
Answer:
x= 100
Step-by-step explanation:
x^2+5x-15000
x^2+150x-100x-15000 x(x+150)-100(x+150) (x+150) or (x-100)
x= -150 or x=100