Answer:
Two real solutions
x =(6-√756)/-10=3/-5+3/5√ 21 = 2.150
x =(6+√756)/-10=3/-5-3/5√ 21 = -3.350
Step-by-step explanation:
Solve Quadratic Equation using the Quadratic Formula
4.3 Solving -5x2-6x+36 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = -5
B = -6
C = 36
Accordingly, B2 - 4AC =
36 - (-720) =
756
Applying the quadratic formula :
6 ± √ 756
x = —————
-10
Can √ 756 be simplified ?
Yes! The prime factorization of 756 is
2•2•3•3•3•7
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 756 = √ 2•2•3•3•3•7 =2•3•√ 21 =
± 6 • √ 21
√ 21 , rounded to 4 decimal digits, is 4.5826
So now we are looking at:
x = ( 6 ± 6 • 4.583 ) / -10
Two real solutions:
x =(6+√756)/-10=3/-5-3/5√ 21 = -3.350
or:
x =(6-√756)/-10=3/-5+3/5√ 21 = 2.150
Two solutions were found :
x =(6-√756)/-10=3/-5+3/5√ 21 = 2.150
x =(6+√756)/-10=3/-5-3/5√ 21 = -3.350
