Use algebra to solve the following equations for x You must

Use algebra to solve the following equations for x. You must show your work ! Give simplified exact answers and also give decimal number answers accurate to three decimal places: a) x (x + 8) = 10 b) |-4x + 3| + 17 = 7x

Solution

a) x(x+8) =10

x^2 +8x -10 =0

Use quadratic root formula :

x = ( -8 +/- sqrt(64 +40) )/2 = -4 +/-sqrt104/2

= -4 +/-sqrt26

b) | -4x +3 | +17 = 7x

(-4x +3) >0

-4x +3 +17 = 7x ; 11x = 20

x = 20/11

(-4x +3)<0

-(-4x +3) +17 = 7x

4x -3 +17 =7x

-3x +14 =0

3x = 14

x = 14/3

Solution: x= 14/3 , 20/11