SOLUTION: HELP PLEASE!! Determine whether the following equation have a solution or not? √2 x² - 4x – 7 √2 = 0''. This is the way I done it but I am not sure if I did the equdra

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Question 186860: HELP PLEASE!! Determine whether the following equation have a solution or not? √2 x² - 4x – 7 √2 = 0''. This is the way I done it but I am not sure if I did the equdratic portion correctly. I get confused on having to divide the equation by 2(√2). The square root is what is confusing me.
2 solutions because the discriminate = 72 which is > 0
b² - 4ac
= (-4)² - 4(√2) (-7√2)
= 16 – 4(2) (-7)
= 72
Solution 1:
X = -b ±√b² - 4ac /2a
X = -(-4) + √72 /2(√2)
X = 4 + 8.485281374 /2.828427125

X = 4.414213562

Solution 2:
X = -b ±√b² - 4ac /2a
X = -(-4) - √72 /2(√2)
X = 4 – 8.485281374/2.828427125
X = -1.585786437



Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
You did great to get the discriminant. The problem only asked is there were solutions; it did not ask what they were. So you went above and beyond. Nice work!
Here's a link you might find handy. http://collabvsl.wetpaint.com/page/Algebra+Solutions
Look at the quadratic section for links to info and a nifty online tool
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1.4142135623731x%5E2%2B-4x%2B-9.89949493661167+=+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=%28-4%29%5E2-4%2A1.4142135623731%2A-9.89949493661167=72.0000000000002.

Discriminant d=72.0000000000002 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+72.0000000000002+%29%29%2F2%5Ca.




Quadratic expression 1.4142135623731x%5E2%2B-4x%2B-9.89949493661167 can be factored:

Again, the answer is: 4.41421356237308, -1.5857864376269. Here's your graph: