7 Find the exact solutions No nonterminating decimals 8 Solv

7.) Find the exact solutions. No non-terminating decimals.

8.) Solve the equation

1/5 x^2 - 3/2 x = 4/10

multiplying entire equation by 10

2x^2 - 15x = 4

subtracting 4 from both sides

2x^2 -15x - 4 = 0

solving the quadratic equation for x

x = { -b + - sqrt ( b^2 - 4ac ) } / 2a

plugging the values

x = { 15 + - sqrt ( 225 - 4(2 *-4) } / 4

x = {15 +- sqrt ( 257 ) } / 4

x = -.258 , x = 7.758

8) 4 = x + sqrt ( 4x - 19 )

subtracting x from both sides

4 - x = sqrt ( 4x - 19 )

squaring both sides to get rid of square root

( 4-x)^2 = 4x - 19

16 + x^2 - 8x = 4x - 19

x^2 -12 x + 35 = 0

solving the equation for x

( x- 7 ) ( x- 5 ) = 0

x = 7 , x = 5

by plugging each solution the equation is not verified

hence , there are no solutions for this equation