Question

Please help me please%20%7B%7D%5E%7B2%7D%20%20-8x%20-%207%20" id="TexFormula1" title=" {x}^{2} + 5x + 4 \\ \\ x {}^{2} -8x - 7 " alt=" {x}^{2} + 5x + 4 \\ \\ x {}^{2} -8x - 7 " align="absmiddle" class="latex-formula">
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Answer 1

Answer:

${x}^{2} + 5x + 4 \\ \\ {x}^{2} + 4x + 1x + 4 \\ \\ x(x + 4) + 1(x + 4) \\ \\ (x + 4)(x + 1) \\ \\ {x}^{2} - 8x - 7 \\ \\ {x}^{2} - 7x + 1x + 7 \\ \\ x(x - 7) + 1( \times - ) \\ \\ (x - 7)(x + 7)$

Answer 2

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Question 1 ~

• ${x}^{2} + 5x + 4$

• ${x}^{2} + 4x + x + 4$

• $x( x + 4) + 1(x + 4)$

• $(x + 4)(x + 1)$

So, the roots are ~

• $\boxed{x = - 4}$

and

• $\boxed{x = - 1}$

Question 2 ~

• ${x}^{2} - 8x - 7$

let's use the quadratic formula for this one ~

(because it can't be solved through middle term split method)

$\boxed{ \mathrm{ \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }}$

where,

• b = -8 (Coefficient of x)

• a = 1 (Coefficient of x²)

• c = -7 (Constant)

now, let's plug the values to find the roots ~

• $\dfrac{ - ( - 8) \pm \sqrt{( - 8) {}^{2} - (4 \times 1 \times - 7) } }{2 \times 1}$

• $\dfrac{8 \pm \sqrt{64 - ( - 28)} }{2}$

• $\dfrac{8 \pm \sqrt{64 + 28} }{2}$

• $\dfrac{8 \pm \sqrt{92} }{2}$

• $\dfrac{8 \pm4 \sqrt{23} }{2}$

• $\dfrac{2(4 \pm2 \sqrt{23)} }{2}$

• $4 \pm2 \sqrt{23}$

So, the roots are ~

• $\boxed{x = 4 + 2 \sqrt{23} }$

and

• $\boxed{x = 4 - 2 \sqrt{23} }$