Solve the following quadratic equations. Be sure to check your solutions.

1. $x^2 − 13x + 42 = 0$

   Step 1(a):

   Draw an area model and diamond. Generic rectangle labeled as follows: Interior upper right box is negative 42. Interior lower left box is X squared. Diamond problem: Left blank, Right blank, Top 42, x squared, Bottom negative 13, x.

   Step 2(a):

   Factor. Added to the rectangle: Interiors: upper left, negative 6, x, & lower right, negative 7, x. Exteriors: left edge, top, negative 6, & bottom, x, bottom edge, left, x, & right, negative 7. Added to the diamond problem: Left negative 6, x, Right negative 7, x.

   Step 3(a):

   $(x − 6)(x − 7) = 0$

   Partial Answer (a):

   $x = 6$.
   Make sure you find the other solution.

   

   

2. $0 = 3x^2 + 10x - 8$

   Hint (b):

   $0 = (3x − 2)(?\: + \:?)$

3. $2x^2 − 10x = 0$

   Hint (c):

   There are only two terms, so factor using the GCF.

4. $4x^2 + 8x − 60 = 0$

   Hint (d):

   Notice that each term is a multiple of $4$.

   Answer (d):

   $x = 3$ or $x = −5$