2 X square + 3x - 90
Answers
2x2+3x-90=0
Two solutions were found :
x = -15/2 = -7.500
x = 6
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(2x2 + 3x) - 90 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 2x2+3x-90
The first term is, 2x2 its coefficient is 2 .
The middle term is, +3x its coefficient is 3 .
The last term, "the constant", is -90
Step-1 : Multiply the coefficient of the first term by the constant 2 • -90 = -180
Step-2 : Find two factors of -180 whose sum equals the coefficient of the middle term, which is 3 .
-180 + 1 = -179
-90 + 2 = -88
-60 + 3 = -57
-45 + 4 = -41
-36 + 5 = -31
-30 + 6 = -24
-20 + 9 = -11
-18 + 10 = -8
-15 + 12 = -3
-12 + 15 = 3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and 15
2x2 - 12x + 15x - 90
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x-6)
Add up the last 2 terms, pulling out common factors :
15 • (x-6)
Step-5 : Add up the four terms of step 4 :
(2x+15) • (x-6)
Which is the desired factorization
Equation at the end of step 2 :
(x - 6) • (2x + 15) = 0
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