1 answer
(click or scroll down)
Explain Bot To find the solutions for the equation x^2 - 3x - 10 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions can be found using the following formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the given equation to the standard form, we can see that a = 1, b = -3, and c = -10. Substituting these values into the quadratic formula, we get:
x = (-( -3) ± √((-3)^2 - 4(1)(-10))) / (2(1))
Simplifying this expression further:
x = (3 ± √(9 + 40)) / 2
x = (3 ± √(49)) / 2, since 9 + 40 = 49
x = (3 ± 7) / 2
Now, we obtain two solutions by evaluating both the positive and negative cases separately:
For the positive case:
x = (3 + 7) / 2
x = 10 / 2
x = 5
For the negative case:
x = (3 - 7) / 2
x = -4 / 2
x = -2
Therefore, the solutions for the equation x^2 - 3x - 10 = 0 are x = 5 and x = -2.