Final answer:
The quadratic equation x²+2x-7=0 is solved using the quadratic formula, resulting in two solutions: x = -1+2√2 and x = -1-2√2.
Step-by-step explanation:
To solve the quadratic equation x²+2x-7=0. The quadratic formula is used to find the roots of any quadratic equation of the form ax²+bx+c=0. The formula is:
x = (-b ± √(b²-4ac)) / (2a)
In this equation a=1, b=2, and c=-7. Plugging these into the quadratic formula:
x = (-(2) ± √((2)²-4(1)(-7))) / (2(1))
x = (-2 ± √(4+28)) / 2
x = (-2 ± √32) / 2
x = (-2 ± 4√2) / 2
Finally, we simplify and get:
x = -1 ± 2√2
Therefore, the solutions to the equation are x = -1+2√2 and x = -1-2√2.