Question

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

x^2 - 4 = 10x

Answer 1

x=10.385 or x= -.385

Explanation:

Given equation is:

x²-4=10x

We have to find the value of x.

x²-4=10x

Adding -10x to both sides of above equation,we get

x²-4-10x=10x-10x

x²-10x-4=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=-10 and c=-4

Putting above values in quadratic formula,we get

x=(-(-10)±√(-10)²-4(1)(-4)) / 2(1)

x=(10±√100+16) / 2

x=(10±√116) / 2

x=(10±10.77) / 2

x= 10+10.77 / 2 or x= 10-10.77 / 2

x=20.77 / 2 or x=-.77 / 2

x=10.385 or x= -.385 is solution of given equation.

Answer 2

The final answers are x = 10.385 OR x = -0.385

Step-by-step explanation:

Given the equation is x^2 -4 = 10x

Rewriting it in quadratic form as:- x^2 -10x -4 = 0.

a = 1, b = -10, c = -4.

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

x = ( 10 ± √(100 -4*1*-4) ) / (2*1)

x = ( 10 ± √(100 +16) ) / (2)

x = ( 10 ± √(116) ) / (2)

x = ( 10 ± 10.77 ) / (2)

x = ( 10 + 10.77 ) / (2) OR x = ( 10 - 10.77 ) / (2)

x = 20.77/2 OR x = -0.77/2

x = 10.385 OR x = -0.385

Hence, final answers are x = 10.385 OR x = -0.385