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) (Show Source): You can put this solution on YOUR website!
Start with the given equation
Subtract 4x from both sides. Add 1 to both sides.
Combine like terms
Let's use the quadratic formula to solve for x:
Starting with the general quadratic
the general solution using the quadratic equation is:
So lets solve ( notice , , and )
Plug in a=1, b=-7, and c=1
Negate -7 to get 7
Square -7 to get 49 (note: remember when you square -7, you must square the negative as well. This is because .)
Multiply to get
Combine like terms in the radicand (everything under the square root)
Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
Multiply 2 and 1 to get 2
So now the expression breaks down into two parts
or
So these expressions approximate to
or
So our solutions are:
or
Notice when we graph , we get:
when we use the root finder feature on a calculator, we find that and .So this verifies our answer
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