Question

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

x^2 - 19 = 9x

Answer 1

x = 10.765 or x= 1.765

Explanation:

Given equation is:

x²-19=9x

We have to find the value of x.

x²-19=9x

Adding -9x to both sides of above equation,we get

x²-4-9x=9x-9x

x²-9x-19=0 eq(1)

ax²+bx+c=0 is general form of quadratic equation.

x= (-b±√b²-4ac) / 2a is quadratic formula to find the value of x.

Comparing eq(1) with general quadratic equation,we get

a=1 b=-9 and c=-19

Putting above values in quadratic formula,we get

x = (-(-9±√(-9)²-4(1)(-19)) / 2(1)

x = (9±√81+76) / 2

x = (9±√157) / 2

x = (9±12.529) / 2

x = (9+12.529) / 2 or (9-12.529) / 2

x= 21.529 / 2 or x= -3.529 / 2

x = 10.765 or x= 1.765 is solution of given equation.

Answer 2

The final answers are x = 10.765 OR x = -1.765

Explanation:

Given the equation is x^2 -19 = 9x

Rewriting it in quadratic form as:- x^2 -9x -19 = 0.

a = 1, b = -9, c = -19.

Using Quadratic formula as follows:- x = ( -b ± √(b² -4ac) ) / (2a)

x = ( 9 ± √(81 -4*1*-19) ) / (2*1)

x = ( 9 ± √(81 +76) ) / (2)

x = ( 9 ± √(157) ) / (2)

x = ( 9 ± 12.53 ) / (2)

x = ( 9 + 12.53 ) / (2) OR x = ( 9 - 12.53 ) / (2)

x = 21.53/2 OR x = -3.53/2

x = 10.765 OR x = -1.765

Hence, final answers are x = 10.765 OR x = -1.765