What is one solution of the equation x² - 21.75x = -15.75?

x² - 21.75x = -15.75

x² - 21.75x + 15.75 = 0 {added 15.75 to each side}

-(-21.75) ± √[(-21.75)² - 4(1)(15.75)]

x = ------------------------------------------------- {substituted into the quadratic formula}

2(1)

21.75 ± √(473.0625 - 63)

x = ---------------------------------- {simplified and evaluated exponent}

2

21.75 ± √410.0625

x = --------------------------- {subtracted under the radical sign}

2

21.75 ± 20.25

x = -------------------- {evaluated square root of 410.0625}

2

21.75 + 20.25 21.75 - 20.25

x = -------------------- or ------------------- {split, using the ± sign}

2 2

42 1.5

x = ------- or ------ {added and subtracted}

2 2

x² - 21.75x + 15.75 = 0 {added 15.75 to each side}

**a = 1, b = -21.75, c = 15.75****-b ± √(b² - 4ac)****x = ----------------------**{the quadratic formula}**2a**-(-21.75) ± √[(-21.75)² - 4(1)(15.75)]

x = ------------------------------------------------- {substituted into the quadratic formula}

2(1)

21.75 ± √(473.0625 - 63)

x = ---------------------------------- {simplified and evaluated exponent}

2

21.75 ± √410.0625

x = --------------------------- {subtracted under the radical sign}

2

21.75 ± 20.25

x = -------------------- {evaluated square root of 410.0625}

2

21.75 + 20.25 21.75 - 20.25

x = -------------------- or ------------------- {split, using the ± sign}

2 2

42 1.5

x = ------- or ------ {added and subtracted}

2 2

**x = 21 or 0.75**{divided}Also, it is possible to find the solutions by using

a graphing calculator.

The

__are the__

**solutions**

**x-intercepts of the graph.**

*- Algebra House*