### Home > AC > Chapter 9 > Lesson 9.2.2 > Problem 9-44

Find the *x*-intercept of the graph using

*two different methods*. The answers from each method should match.

To find the *x*-intercepts, make *y* = 0.

Method 1:

Draw a generic rectangle and diamond.

Labels added to generic rectangle, interior top right, negative 6, interior bottom left, 5 x squared. Labels added to diamond, top, negative 30 x squared, bottom, 7 x. Set *y* = 0.

0 = 5*x*² + 7*x* − 6

The missing numbers in the square should equal 7*x*.

Labels added to generic rectangle, interior top left, 10 x, interior bottom right, negative 3 x, Labels added to diamond, left, 10 x, right, negative 3 x.

0 = (*x* + 2)(5*x* − 3)

Labels added to generic rectangle, left edge top, 2, left edge bottom, x, bottom edge left, 5 x, bottom edge right, negative 3.

*x* + 2 = 0 or 5*x* − 3 = 0

*x* = −2

Method 2:

Substitute the *a*, *b*, and *c* values of the expression into the quadratic formula.

Finish the rest yourself and show that both methods give the same answer.