SOLUTION: Solve the equation using the quadratic formula. 4x^2 - 23x - 6 = 0
Quadratic Equations and Parabolas
-> SOLUTION: Solve the equation using the quadratic formula. 4x^2 - 23x - 6 = 0
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Solve the equation using the quadratic formula.
4x^2 - 23x - 6 = 0
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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
Plug in a=4, b=-23, and c=-6
Negate -23 to get 23
Square -23 to get 529 (note: remember when you square -23, you must square the negative as well. This is because
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
Multiply 2 and 4 to get 8
So now the expression breaks down into two parts
Lets look at the first part:
Add the terms in the numerator
So one answer is
Now lets look at the second part:
Subtract the terms in the numerator
So another answer is
So our solutions are: