Finding solutions to a quadratic equation

2/18/2015

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}

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}