Question

transform (s+6)²=15 into quadratic equation in the form at ax²+bx+c=0 and sove for it's solution​

Answer 1

Answer:

(s+6)²=15 into quadratic equation in the form

ax²+bx+c=0

${s}^{2} + 12s + 36 = 15$

${s}^{2} + 12s + 21 = 0$

And the solution is,

$s = \sqrt{15} - 6$

Answer 2

Given,

$\[{\left( {s + 6} \right)^2} = 15\]$

Standard quadratic equation, $\[a{x^2} + bx + c = 0\]$

Solution,

Convert the given equation in quadratic equation.

$\[\begin{array}{l}{\left( {s + 6} \right)^2} = 15\\ \Rightarrow {s^2} + 12s + 36 = 15\\ \Rightarrow {s^2} + 12s + 21 = 0\end{array}\]$

Compare the standard quadratic equation.

$\[a = 1,b = 12,c = 21\]$

Use Shri Dharacharya Formula for solution,

$\[s= \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\]$

$\[ \Rightarrow s= \frac{{ - 12 \pm \sqrt {{{12}^2} - 4 \times 1 \times 21} }}{{2 \times 1}}\]$

$\[ \Rightarrow s = \frac{{ - 12 \pm \sqrt {60} }}{2}\]$

$\[ \Rightarrow s = - 6 \pm \sqrt {15} \]$

Hence the solution are $\[ - 6 \pm \sqrt {15} \]$