Enter your answer and show all the steps that you use to solve this problem in the space provided. Use the quadratic formula to solve the equation x2−4x−3=0
To solve the quadratic equation x^2 - 4x - 3 = 0 using the quadratic formula, we first identify the coefficients of the terms.
The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -4, and c = -3.
Now we can substitute these values into the quadratic formula:
x = (-(-4) ± √((-4)^2 - 4(1)(-3))) / (2(1))
x = (4 ± √(16 + 12)) / 2
x = (4 ± √28) / 2
Next, we simplify the expression under the square root:
x = (4 ± √4 * √7) / 2
x = (4 ± 2√7) / 2
We can simplify this further by dividing both terms by 2:
x = 2 ± √7
So the solutions to the equation x^2 - 4x - 3 = 0 using the quadratic formula are:
x = 2 + √7
or
x = 2 - √7