Final answer:
The quadratic equation x²+6x-7=0 is solved using the quadratic formula, yielding the solutions x = 1 and x = −7.
Step-by-step explanation:
The equation x²+6x-7=0 is a quadratic equation, which is in the form ax²+bx+c=0.
To solve this equation, we can use the quadratic formula which is:
x = −b ± √(b² - 4ac) / (2a)
In our equation, a=1, b=6, and c= −7.
Substituting the values into the formula:
x = −6 ± √((6)² - 4(1)(−7)) / (2(1))
x = −6 ± √(36 + 28) / 2
x = −6 ± √64 / 2
x = −6 ± 8 / 2
Thus, the solutions are:
- x = (−6 + 8)/2 = 1
- x = (−6 - 8)/2 = −7
Therefore, the solutions or roots of the equation are x = 1 and x = −7.