Write this out as you read it; We'll call one of the numbers N and the other M;

N + M = 20

N

Now we have two equations, two unknowns. We should be able to solve this.

If N + M = 20, then M = 20 - N

Substitute M into the second equation

N

now solve for N. begin by expanding the binomial;

N

Then collect terms to simplify

2N

we can divide all the way through by 2

N

Let's just plug this into the quadratic formula and solve.

-B +/- sqrt(B

______

In this case, A = 1, B = -20, C = 91

20 +/- sqrt(400 - 4 * 91)

______

20 +/- 6

______

the roots are 13, and 7.

7 + 13 = 20 is true, so far, so good.

7

49 + 169 = 218 is true as well,

so those are both of the numbers.

N + M = 20

N

^{2}+ M^{2}= 218Now we have two equations, two unknowns. We should be able to solve this.

If N + M = 20, then M = 20 - N

Substitute M into the second equation

N

^{2}+ (20 - N)^{2}= 218now solve for N. begin by expanding the binomial;

N

^{2}+^{}400 - 40N + N^{2}= 218Then collect terms to simplify

2N

^{2}-40N + 182 = 0we can divide all the way through by 2

N

^{2}-20N + 91 = 0Let's just plug this into the quadratic formula and solve.

-B +/- sqrt(B

^{2}- 4AC)______

2A

In this case, A = 1, B = -20, C = 91

20 +/- sqrt(400 - 4 * 91)

______

2

20 +/- 6

______

2

the roots are 13, and 7.

7 + 13 = 20 is true, so far, so good.

7

^{2}+ 13^{2}= 21849 + 169 = 218 is true as well,

so those are both of the numbers.