Evaluate: integral of (sin(x)+cos(x))^2 x

Expression: b^2+16 b+64=0

Write the problem as a mathematical expression

$b^{2} + 16b + 64 = 0$

Rewrite $64$

$b^{2} + 16b + 8^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term

$16b = 2 \cdot b \cdot 8$

Rewrite the polynomial

$b^{2} + 2 \cdot b \cdot 8 + 8^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} + 2ab + b^{2} = \left(a + b\right)^{2}$

$\left(b + 8\right)^{2} = 0$

Set the $b + 8$

$b + 8 = 0$

Subtract $8$

$b = - 8$