How do you solve #x^2 – 4x – 5 = 0# using the quadratic formula?

Question

Abigail Allen · Accepted Answer

# x= 5,-1 # Use the quadratic formula for : #ax^2+bx+c# # x = (-b +- sqrt( b^2 - 4ac) ) /(2a) # # x = (( 4 +- sqrt( 16- 4(1)(-5))) /(2*(1)) # # x = ((4+- sqrt(36) )/(2)) # # x = 2+-3 # # x= 5, -1 #

Julia Adams · Answer

undefined To solve the quadratic equation $x^2 - 4x - 5 = 0$ using the quadratic formula, where $a = 1$, $b = -4$, and $c = -5$, follow these steps:

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

2. Calculate the discriminant, $D = b^2 - 4ac$.

3. Substitute the values of $a$, $b$, and $D$ into the quadratic formula.

4. Simplify the expression.

5. Solve for $x$.

6. Determine the solutions for $x$ by considering both the positive and negative square roots.

Applying these steps:

1. $D = (-4)^2 - 4(1)(-5) = 16 + 20 = 36$.

2. $x = \frac{{-(-4) \pm \sqrt{{36}}}}{{2(1)}}$.

3. $x = \frac{{4 \pm 6}}{{2}}$.

4. $x = \frac{{4 + 6}}{{2}}$ or $x = \frac{{4 - 6}}{{2}}$.

5. $x = \frac{{10}}{{2}}$ or $x = \frac{{-2}}{{2}}$.

6. $x = 5$ or $x = -1$.

Therefore, the solutions for $x$ are $x = 5$ and $x = -1$.

Julia Adams · Answer

undefined To solve the quadratic equation $x^2 - 4x - 5 = 0$ using the quadratic formula, $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$, where $a$, $b$, and $c$ are the coefficients of $x^2$, $x$, and the constant term, respectively:

1. Identify the coefficients: $a = 1$, $b = -4$, $c = -5$.
2. Substitute the values into the quadratic formula: $x = \frac{{-(-4) \pm \sqrt{{(-4)^2 - 4(1)(-5)}}}}{{2(1)}}$.
3. Simplify: $x = \frac{{4 \pm \sqrt{{16 + 20}}}}{2}$.
4. Further simplify: $x = \frac{{4 \pm \sqrt{{36}}}}{2}$.
5. Calculate the square root: $\sqrt{36} = 6$.
6. Substitute the square root result: $x = \frac{{4 \pm 6}}{2}$.
7. Calculate the two possible solutions:
   a. $x = \frac{{4 + 6}}{2} = \frac{{10}}{2} = 5$.
   b. $x = \frac{{4 - 6}}{2} = \frac{{-2}}{2} = -1$.
So, the solutions are $x = 5$ and $x = -1$.