How would u solve/simplify
d+12=d^2
I also need help on
-4z^2+z+5=0
To solve the equation d + 12 = d^2, you can follow these steps:
1. Rearrange the equation so that one side is equal to zero: d^2 - d - 12 = 0
(Subtract d and 12 from both sides)
2. Factorize the quadratic equation (if possible) or use the quadratic formula:
In this case, the equation can be factored as (d - 4)(d + 3) = 0.
3. Set each factor equal to zero and solve for d:
d - 4 = 0 or d + 3 = 0
Solving these individual equations will give two possible solutions:
d = 4 or d = -3
So, the solutions to the equation d + 12 = d^2 are d = 4 and d = -3.
Now, let's move on to the second question:
To solve the equation -4z^2 + z + 5 = 0, you can use the quadratic formula:
1. Identify the coefficients of the quadratic equation:
Here, a = -4, b = 1, and c = 5.
2. Apply the quadratic formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the given values, we get:
z = (-(1) ± √((1)^2 - 4(-4)(5))) / (2(-4))
3. Simplify the expression under the square root:
Evaluate the expression inside the square root to determine whether it is positive or negative.
√((1)^2 - 4(-4)(5)) simplifies to √(1 + 80) = √81 = 9
4. Plug in the simplified values into the quadratic formula:
z = (-(1) ± 9) / (-8)
This gives two possible solutions:
z = (1 + 9) / -8 = 10 / -8 = -5/4
z = (1 - 9) / -8 = -8 / -8 = 1
Therefore, the solutions to the equation -4z^2 + z + 5 = 0 are z = -5/4 and z = 1.