Fill in the parts -whole model for the following equation. (-8x^2-5x-5)+(underline ( ))=-16x^2+5x-12 ) =-16x?+5z-12 square square square

To fill in the parts-whole model for the given equation, we need to find the missing expression that, when added to $(-8x^{2}-5x-5)$, equals $-16x^{2}+5x-12$.<br /><br />Let's denote the missing expression as $(ax^2 + bx + c)$.<br /><br />So, the equation becomes:<br />$(-8x^{2}-5x-5) + (ax^2 + bx + c) = -16x^{2}+5x-12$<br /><br />Now, let's compare the coefficients of the corresponding terms on both sides of the equation:<br /><br />For the $x^2$ terms:<br />$-8x^2 + ax^2 = -16x^2$<br />$-8 + a = -16$<br />$a = -8$<br /><br />For the $x$ terms:<br />$-5x + bx = 5x$<br />$-5 + b = 5$<br />$b = 10$<br /><br />For the constant terms:<br />$-5 + c = -12$<br />$c = -7$<br /><br />Therefore, the is $(-8x^2 + 10x - 7)$.<br /><br />So, the parts-whole model for the given equation is:<br />$(-8x^{2}-5x-5) + (-8x^2 + 10x - 7) = -16x^{2}+5x-12$