SOLUTION: solve using the quadratic formula: 9x(sqaured) + 8=44 solve using the quadratic formula: 3x(squared)- 5x-4 = 0 Solve for z: z(squared)-8z=9 Solve the square root of: x-1=-3

Algebra ->  Radicals -> SOLUTION: solve using the quadratic formula: 9x(sqaured) + 8=44 solve using the quadratic formula: 3x(squared)- 5x-4 = 0 Solve for z: z(squared)-8z=9 Solve the square root of: x-1=-3      Log On


   

Question 350672: solve using the quadratic formula: 9x(sqaured) + 8=44
solve using the quadratic formula: 3x(squared)- 5x-4 = 0
Solve for z: z(squared)-8z=9
Solve the square root of: x-1=-3
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
.
9x%5E2+-36+=+0
9%28x%5E2+-4%29+=+0
(x + 2)(x-2)= 0
x = 2 or x= -2
.
z%5E2+-+8z+-9%29
(z-9)(z+1)
z = 9 or z = -1
.
sgrt%28x-1%29+=+-3
(x-1) = 9
x = 10
.
3x^2 -5x -4 =0
Use quadratic formula
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-5x%2B-4+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-5%29%5E2-4%2A3%2A-4=73.

Discriminant d=73 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+73+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+73+%29%29%2F2%5C3+=+2.25733395755292
x%5B2%5D+=+%28-%28-5%29-sqrt%28+73+%29%29%2F2%5C3+=+-0.590667290886255

Quadratic expression 3x%5E2%2B-5x%2B-4 can be factored:
3x%5E2%2B-5x%2B-4+=+3%28x-2.25733395755292%29%2A%28x--0.590667290886255%29
Again, the answer is: 2.25733395755292, -0.590667290886255. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-5%2Ax%2B-4+%29