Explain Why The Equation(X-2)^2-40=9 Has Two Solutions. Then Solve The Equation To Find The Solutions. Show All Work

Explain why the equation(x-2)^2-40=9 has two solutions. Then solve the equation to find the solutions. SHOW ALL WORK

 

Answer:

x = 9  or x = -5

Step-by-step explanation:

A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions.

First, make the equation into standard form: ax² + bx + c = 0

(x-2)^2 - 40=9

(x² -4x + 4 ) - 40 = 9

combine like terms

x² -4x -36 -9 = 0

x² - 4x -45 = 0    

x² + (-4x) + (-45) = 0    

a = 1

b = -4

c = -45

use quadratic formula

x = -b ± √(b² - 4ac) / 2a

x = {4 ± √(-4)² - 4(1)(-45) }/ 2(1)

x = 4 ± √(16 + 180) / 2

x = 4 ± √(196) / 2

x = 4 ± 14/ 2

x = 2 ± 7

x = 9  or x = -5 (therefore, any quadratic equation or degree of 2 has two solutions)