Final answer:
To solve the quadratic equation x²+10x+8=0, we use the quadratic formula with a=1, b=10, and c=8 to find two possible solutions for x, which are approximately -0.877 and -9.123.
Step-by-step explanation:
To solve for x in the quadratic equation x²+10x+8=0, we apply the quadratic formula, which is x = (-b ± √(b²-4ac))/(2a) where a, b, and c are coefficients from the equation ax²+bx+c = 0. In our case, a=1, b=10, and c=8. Plugging these into the quadratic formula, we have:
x = (-10 ± √(10²-4(1)(8)))/(2(1))
x = (-10 ± √(100-32))/2
x = (-10 ± √68)/2
Since √68 is approximately 8.246, we simplify to get two possible solutions for x:
x = (-10 + 8.246)/2 or x = (-10 - 8.246)/2
x ≈ -0.877 or x ≈ -9.123
Therefore, the two solutions for x are approximately -0.877 and -9.123.