Question

2x2 − 1 = 3x + 4 Which equation correctly applies the quadratic formula?

Answer 1

Standard form: ax^2 + bx + c = y

Steps to simplify:

2x^2 - 1 = 3x + 4

~Subtract (3x + 4) to both sides

2x^2 - 1 - 3x + 4 = 3x + 4 - 3x + 4

~Simplify

2x^2 - 3x - 5 = 0

(a = 2, b = -3, c = -5)

Now that we know what these values are, we can use the quadratic formula to solve.

$x=\frac{-b-+\sqrt{b^2-4ac} }{2a} \\x = \frac{-(-3)-+\sqrt{-3^2-4(2)(-5)} }{2(2)}\\x= \frac{-3-+\sqrt{49} }{4} \\x=\frac{3-+7}{4} \\x = \frac{10}{4}~or~\frac{-4}{4} \\x=\frac{5}{2}~or~-1$

Answer: x = 5/2 or x = -1

Best of Luck!