Solving quadratic equations using the quadratic formula

Question

X^2=4z+1

Answer 1

Assuming that "z" should be "x", we have:

x² - 4x - 1 = 0

x = [-(-4) ± √[(-4)² - 4(1)(-1)] ] / (2(1)) = (4 ± √20) / 2 = [4 ± √((4)(5))]/ 2 = [4 ± 2√5] / 2

= 2(2 ± √5) / 2 = 2 ± √5 = 2 - √5 , 2 + √5

Answer 2

Great question! First, we must rewrite the equation so that the variables are in order from the largest exponent to the smallest on one side of the equal sign:

1. x² = 4z +1 → x² - 4z - 1 = 0

Next, we determine which exponent corresponds to which variable in the quadratic equation:

1. ax² + bx + c = 0: general equation
2. 1x² = ax², so a = 1
3. -4z = bx, so b = -4
4. -1 = c, so c = -1

Next, we plug each of the three variables into the general quadratic formula:

1. x = (-b ± √b² - 4ac) / 2a
2. x = (-(-4) ± √(-4)² - 4(1)(-1)) / 2(1)

Next, we simplify the equation:

1. x = (4 ± √16 - (-4)) / 2
2. x = (4 ± √16 + 4) / 2
3. x = (4 ± √20) / 2
4. x = (4 ± 4.472135955) / 2
5. x = (4 + 4.472) / 2 AND x = (4 - 4.472) / 2
6. x = 8.472 / 2 AND x = -0.472 / 2
7. x = 4.236 AND x = -0.236

In conclusion, the two possible solutions for x are 4.236 and -0.236.

Answer 3

Hello! For the equation x^2=4x+1, first rearrange it to x^2-4x-1=0

Now according to the quadratic equation ax^2+bx+c=0, we can see that a=1, b=(-4) and c=(-1)

To solve, plug these into the formula

So therefore x=(4+/- square root of 20) / 2

X=4.236 or X=(-0.236)