Final answer:
The quadratic equation x²+3x-7=0 can be solved using the quadratic formula to find the exact solutions (-3 + √37) / 2 and (-3 - √37) / 2. The approximate solutions for x are 1.54 and -4.54.
Step-by-step explanation:
To solve the quadratic equation x²+3x-7=0, we can use the quadratic formula x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients from the quadratic equation of the form ax²+bx+c=0. In this case, a=1, b=3, and c=-7. Plugging these values into the quadratic formula gives us:
- x = (-3 ± √(3² - 4(1)(-7))) / (2(1))
- x = (-3 ± √(9+28)) / 2
- x = (-3 ± √37) / 2
Thus, x equals to the two solutions (-3 + √37) / 2 and (-3 - √37) / 2. To get approximate values, we can calculate the square root of 37 and divide the sum and difference by 2:
- x ≈ (-3 + 6.08) / 2 ≈ 1.54
- x ≈ (-3 - 6.08) / 2 ≈ -4.54
The exact solutions are (-3 + √37) / 2 and (-3 - √37) / 2, and the approximate solutions are 1.54 and -4.54.