SOLUTION: 5. Solve using the quadratic formula: x^2 – 3x = 4x – 1

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Question 132985This question is from textbook intermediate algebra
: 5. Solve using the quadratic formula:
x^2 – 3x = 4x – 1
 This question is from textbook intermediate algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-3x=4x-1 Start with the given equation


x%5E2-3x-4x%2B1=0 Subtract 4x from both sides. Add 1 to both sides.


x%5E2-7x%2B1=0 Combine like terms



Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve x%5E2-7%2Ax%2B1=0 ( notice a=1, b=-7, and c=1)




x+=+%28--7+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29 Plug in a=1, b=-7, and c=1



x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29 Negate -7 to get 7



x+=+%287+%2B-+sqrt%28+49-4%2A1%2A1+%29%29%2F%282%2A1%29 Square -7 to get 49 (note: remember when you square -7, you must square the negative as well. This is because %28-7%29%5E2=-7%2A-7=49.)



x+=+%287+%2B-+sqrt%28+49%2B-4+%29%29%2F%282%2A1%29 Multiply -4%2A1%2A1 to get -4



x+=+%287+%2B-+sqrt%28+45+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%287+%2B-+3%2Asqrt%285%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%287+%2B-+3%2Asqrt%285%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%287+%2B+3%2Asqrt%285%29%29%2F2 or x+=+%287+-+3%2Asqrt%285%29%29%2F2



So these expressions approximate to

x=6.85410196624968 or x=0.145898033750315


So our solutions are:
x=6.85410196624968 or x=0.145898033750315

Notice when we graph x%5E2-7%2Ax%2B1, we get:



when we use the root finder feature on a calculator, we find that x=6.85410196624968 and x=0.145898033750315.So this verifies our answer