How do you solve $\sqrt{3 m + 28} = m$ $sqrt(3m+28) =m$ ?

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How do you solve $\sqrt{3 m + 28} = m$ $sqrt(3m+28) =m$ ?

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Answer 1 · 2015-07-20T15:00:15

$m = 7$ $color(blue)( m=7$

Explanation:

$\sqrt{3 m + 28} = m$ $sqrt(3m+28) =m$

Squaring both sides
${(\sqrt{3 m + 28})}^{2} = m^{2}$ $(sqrt(3m+28))^2 =m^2$

$3 m + 28 = m^{2}$ $3m +28=m^2$

$m^{2} - 3 m - 28 = 0$ $m^2 - 3m -28=0$

Factorising by splitting the middle term (in order to find the solutions)**

$m^{2} - 3 m - 28 = 0$ $m^2 - color(green)(3m) -28=0$

$m^{2} - 7 m + 4 m - 28 = 0$ $m^2 - color(green)(7m +4m) -28=0$

$m (m - 7) + 4 (m - 7) = 0$ $m(m-7) +4 (m-7)=0$

$(m + 4) (m - 7) = 0$ $(m+4)(m-7) =0$

**Upon equating the factors with zero we can obtain solutions:
**
$m + 4 = 0, m = - 4$ $m+4=0, m=-4$
This solution is not applicable as square root of an expression cannot be negative

So the solution is
$(m - 7) = 0, m = 7$ $(m-7) =0, m=7$

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How do you solve $\sqrt{3 m + 28} = m$ $sqrt(3m+28) =m$ ?

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How do you solve $\sqrt{3 m + 28} = m$ $sqrt(3m+28) =m$ ?