what is the answer to this problem 4x^2-4x-3=0
Let's use the quadratic formula to solve this.
b (plus or minus) sqrt(b^2 - 4ac)
x = -----------------------------------------
2a
I apologize for the poor way I had to write that. There
is a math symbol which means (plus or minus); it is a
plus sign sitting on top of a minus sign. It means that
two operations are indicated. First, you add the result
of the square root operation to b before dividing by 2a;
second, you subtract the result of the square root operation
from b before dividing by 2a. Follow along; it will become
clear.
a, b and c are the constants found on the left side of the
equation 4x2-4x-3=0. a sits in front of x^2, b sits in front of
x, and c is the -3.
Let's tackle that square root first. Solve the operations inside
the sqrt bracket: b^2 - 4ac
b^2 - 4ac = (-4)^2 - 4(4)(-3) = 16 - (-48) = 64
Taking the square root of that gives us 8.
Now, we will solve both possibilities in the numerator,
(b + 8) and (b - 8)
4 + 8 = 12 4 - 8 = -4
We'll hold those in reserve while we solve the denominator,
(2a). That's 2 * 4 = 8.
We have two fractions, (12 / 8) and (-4 / 8).
Those are 1.5 and -0.5
Going back to the quadratic formula, we have
x = 1.5 and x = -0.5 as solutions to the original problem.
We are not finished until we verify the solutions.
Start with x = 1.5.
4 x^2 - 4x - 3 = 0
4 * (1.5 * 1.5) - 4 * (1.5) - 3 = 0
4 * 2.25 - 6 - 3 = 0
9 - 6 - 3 = 0
We can see that that solution works.
Now try x = -0.5
4 x^2 - 4x - 3 = 0
4 * (-0.5 * -0.5) - 4 * (-0.5) - 3 = 0
4 * (0.25) - (-2) - 3 = 0
1 + 2 - 3 = 0
That solution works, too.
So the answer to the problem is x = 1.5 and x = -0.5
To clear up any confusion, this problem has given you the
formula for a parabola that crosses the x axis at two points,
(-0.5, 0) and (1.5, 0). The parabola opens upward, and the
vertex is at (1, -4)