1. 7v^2 - 48v - 7 = 0
2. 9h^2 - 15h + 4 = 0
3. 25x^2 + 10x + 1 = 0
I'm just stuck on these three questions, because they have a number in front of the letter. Can someone show me how to do them?
Thanks!
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answers:
JG say: All quadratic equations are in the form ax^2 + bx + c = 0 where a, b and c are the coeffiicents.
The quadratic formula is x = [-b ± √(b^2 - 4ac)]/(2a)
1. 7v^2 - 48v - 7 = 0
a = 7, b = -48, c = -7
x = [-b ± √(b^2 - 4ac)]/(2a) = [-(-48) ± √((-48)^2 - 4(7)(-7)]/ [2(7)] = (48 ± √2500)/(14) = (48 ± 50)/14 = (24±25)/7
x = (24+25)/7 = 49/7 = 7 or x = (24-25)/7 = -1/7
2. 9h^2 - 15h + 4 = 0
a = 9, b = -15, c = 4
x = [-b ± √(b^2 - 4ac)]/(2a) = [-(-15) ± √[(-15)^2 - 4(9)(4)])]/(2*9) = (15 ± √81)/18 = (15±9)/18 = (5±3)/6
x = (5+3)/6 = 8/6 = 4/3 or x = (5-3)/6 = 2/6 = 1/3
3. 25x^2 + 10x + 1 = 0
a = 25, b = 10, c = 1
x = [-b ± √(b^2 - 4ac)]/(2a) = [-10 ± √(10^2 - 4(25)(1))]/(2*25) = (-10 ± 0)/50 = -10/50 = -1/5
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Melissa say: to solve quadratic equations using the formula all you do is take your quadratic equation ax^2 + bx + c = 0 and plug the values for a,b,c into (-b +/- sqrt(b^2 - 4ac))/(2a) into the formula...
you might find this video helpful...
bear in mind though just 'cause there's a value awesomeer than one in front of the x squared term doesn't mean you for the life of me cannot factorise it...
look for two numbers that multiply to give 7*-7 = -49 and add together to give -48, clearly that's -49 and 1... now decompose your x terms into -49x + x... so our first equation becomes:
7v^2 - 49v + v -7 = 0
now factor the first and last two terms...
7v(v-7) + 1(v-7) = 0
now factor the common term...
(v-7)(7v+1) = 0
so either v-7 = 0 or 7v+1 = 0