Question #270b3

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Question #270b3

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Answer 1 · 2017-12-14T22:38:16

$v = - 6 or v = 1$ $v=-6" or "v=1$

Explanation:

$rearrange and equate to zero$ $"rearrange and equate to zero"$

$\Rightarrow 7 v^{2} + 35 v - 42 = 0 \leftarrow standard form$ $rArr7v^2+35v-42=0larrcolor(blue)"standard form"$

$take out a common factor of 7$ $"take out a "color(blue)"common factor of 7"$

$\Rightarrow 7 (v^{2} + 5 v - 6) = 0$ $rArr7(v^2+5v-6)=0$

$the factors of - 6 which sum to + 5 are + 6 and - 1$ $"the factors of - 6 which sum to + 5 are + 6 and - 1"$

$\Rightarrow 7 (v + 6) (v - 1) = 0$ $rArr7(v+6)(v-1)=0$

$equate each factor to zero and solve for v$ $"equate each factor to zero and solve for v"$

$v + 6 = 0 \Rightarrow v = - 6$ $v+6=0rArrv=-6$

$v - 1 = 0 \Rightarrow v = 1$ $v-1=0rArrv=1$

$the solutions are v = - 6 or v = 1$ $"the solutions are "v=-6" or "v=1$

Answer 2 · 2017-12-14T22:40:32

$v = 1 or - 6$ $v=1 or -6$

Explanation:

$7 v^{2} - 42 = - 35 v$ $7v^2 -42 = -35v$

$7 v^{2} + 35 v - 42 = 0$ $7v^2+35v -42 = 0$

$7 (v^{2} + 5 - 6) = 0$ $7(v^2+5-6)=0$

$v^{2} + 5 - 6 = 0$ $v^2+5-6=0$

$(v + 6) (v - 1) = 0$ $(v+6)(v-1)=0$

Using the 0 product property (if $a b = 0$ $ab=0$ , then $a = 0 or b = 0$ $a =0 or b= 0$ )

$v + 6 = 0$ $v+6=0$
$\Rightarrow v = - 6$ $=>v=-6$

$v - 1 = 0$ $v-1=0$
$v = 1$ $v=1$

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Question #270b3

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