24x^2 - 334x - 135=0
Answers
x = 5/12 = 0.417
x = 27/2 = 13.500
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((23•3x2) - 334x) + 135 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 24x2-334x+135
The first term is, 24x2 its coefficient is 24 .
The middle term is, -334x its coefficient is -334 .
The last term, "the constant", is +135
Step-1 : Multiply the coefficient of the first term by the constant 24 • 135 = 3240
Step-2 : Find two factors of 3240 whose sum equals the coefficient of the middle term, which is -334 .
-3240 + -1 = -3241
-1620 + -2 = -1622
-1080 + -3 = -1083
-810 + -4 = -814
-648 + -5 = -653
-540 + -6 = -546
-405 + -8 = -413
-360 + -9 = -369
-324 + -10 = -334 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -324 and -10
24x2 - 324x - 10x - 135
Step-4 : Add up the first 2 terms, pulling out like factors :
12x • (2x-27)
Add up the last 2 terms, pulling out common factors :
5 • (2x-27)
Step-5 : Add up the four terms of step 4 :
(12x-5) • (2x-27)
Which is the desired factorization
Equation at the end of step 2 :
(2x - 27) • (12x - 5) = 0
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