Final answer:
To solve the equation x^2-x-3=x using the quadratic formula, rearrange the equation to the standard quadratic form and substitute the values into the quadratic formula to solve for x. The solutions to the equation are x = 3 and x = -1.
Step-by-step explanation:
To solve the equation x^2-x-3=x using the quadratic formula, we need to first rearrange the equation to a standard quadratic form by bringing all terms to one side:
x^2 - x - 3 - x = 0
Simplifying the equation, we get:
x^2 - 2x - 3 = 0
The quadratic formula is given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Comparing the equation to the standard form ax^2 + bx + c = 0, we have a = 1, b = -2, and c = -3.
Substituting these values into the quadratic formula, we can solve for x.
x = (-(-2) ± sqrt((-2)^2 - 4(1)(-3))) / (2(1))
Simplifying further, we get:
x = (2 ± sqrt(4 + 12)) / 2
x = (2 ± sqrt(16)) / 2
x = (2 ± 4) / 2
Therefore, the solutions to the equation are x = 3 and x = -1.