Final answer:
To solve the inequality x² +8x-7<0, use the quadratic formula to find the roots of the equation. These roots are the critical values that separate the number line. Test intervals between these critical values to find where the quadratic expression is negative, providing the solution set.
Step-by-step explanation:
To solve the inequality x² +8x-7<0, we look for values of x that make the quadratic expression negative. This requires finding the roots of the equation x² + 8x - 7 = 0 which can be done by applying the quadratic formula: x = [-b ± √(b² - 4ac)] / (2a). In this case, a = 1, b = 8, and c = -7.
Calculating the discriminant gives us √(64 + 28) = √92. Thus, the roots are x = [-8 ± √92] / 2. These roots split the number line into intervals. We then test a value from each interval in the inequality to see which intervals satisfy the condition. The solution to the inequality will be the interval or intervals where the quadratic expression yields a negative value.