Final answer:
To solve the equation x²+2x+1=17, we can use the quadratic formula to find the values of x. The solutions are x = -1 + √17 and x = -1 - √17.
Step-by-step explanation:
To solve the equation x²+2x+1=17, we can rearrange it as x²+2x-16=0. This is a quadratic equation, so we can use the quadratic formula to solve for x. The quadratic formula is x = (-b ± √(b²-4ac))/(2a).
Plugging in the values from our equation, we get x = (-2 ± √(2²-4(1)(-16)))/(2(1)). Simplifying further gives x = (-2 ± √(4+64))/2 and x = (-2 ± √68)/2.
Since we're looking for real solutions, we can simplify x = (-2 ± 2√17)/2 to x = -1 ± √17.