Question

delta distribute and factor 100% credit until: november 3 at 11:59 pm grade: 27% squaring simple binomials scientific calculator graphing calculator jefferson mejia medina log out write two numbers that multiply to the value on top and add to the value on bottom. answer attempt 1 out of 2 13 +× 36

Explanation:

Step1: Set up equations

Let the two numbers be $x$ and $y$. We know that $xy = 36$ and $x + y=13$. From $x + y = 13$, we can express $y=13 - x$. Substitute $y = 13 - x$ into $xy = 36$, we get $x(13 - x)=36$.

Step2: Expand and solve the quadratic - equation

Expand $x(13 - x)=36$ to $13x-x^{2}=36$, or $x^{2}-13x + 36=0$.
For a quadratic equation $ax^{2}+bx + c = 0$ (here $a = 1$, $b=-13$, $c = 36$), we use the quadratic formula $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. First, calculate the discriminant $\Delta=b^{2}-4ac=(-13)^{2}-4\times1\times36=169 - 144 = 25$. Then $x=\frac{13\pm\sqrt{25}}{2}=\frac{13\pm5}{2}$.

Step3: Find the two solutions

When we take the plus - sign: $x=\frac{13 + 5}{2}=9$. When we take the minus - sign: $x=\frac{13-5}{2}=4$.
If $x = 9$, then $y = 4$; if $x = 4$, then $y = 9$.

Answer:

4, 9