How do you solve using the quadratic formula #x^2-5x-14=0#?

Question

Genesis Allen · Accepted Answer

#y = x^2 - 5x - 14 = 0# D = d^2 = 25 + 56 = 81  -> d = +-9 x = 5/2 + 9/2 = 14/2 = 7 x = 5/2 - 9/2 = -4/2 = -2 There is another way that is faster. (new AC Method)
Find 2 numbers knowing product (-14) and sum (7). Compose factor pairs of (-14): (-1, 14)(-2, 7). This last sum is 5 = -b. Then the 2 real roots are: -2 and 7

Hazel Anglin · Answer

undefined To solve the quadratic equation $ x^2 - 5x - 14 = 0 $ using the quadratic formula, follow these steps:

1. Identify the coefficients of the quadratic equation: $ a = 1 $, $ b = -5 $, and $ c = -14 $.

2. Substitute the values of $ a $, $ b $, and $ c $ into the quadratic formula:
$$ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} $$

3. Plug in the values:
$$ x = \frac{{-(-5) \pm \sqrt{{(-5)^2 - 4(1)(-14)}}}}{2(1)} $$

4. Simplify inside the square root:
$$ x = \frac{{5 \pm \sqrt{{25 + 56}}}}{2} $$
$$ x = \frac{{5 \pm \sqrt{{81}}}}{2} $$

5. Simplify further:
$$ x = \frac{{5 \pm 9}}{2} $$

6. Solve for both possible solutions:
$$ x_1 = \frac{{5 + 9}}{2} = 7 $$
$$ x_2 = \frac{{5 - 9}}{2} = -2 $$

Therefore, the solutions to the quadratic equation $ x^2 - 5x - 14 = 0 $ are $ x = 7 $ and $ x = -2 $.