What is the solution to x3=−343?(1 point)
Responses
x=343−−−√2
x equals root index 2 Start Root 343 End Root
x=343−−−√3
x equals root index 3 Start Root 343 End Root
x=−343−−−−√3
x equals root index 3 Start Root negative 343 End Root
x=−−343−−−−√3
x equals negative root index 3 Start Root negative 343 End Root
x=−7
To solve the equation x^3 = -343, we can find the cube root of -343.
The cube root of -343 is -7, because (-7)^3 equals -343.
Therefore, the solution to the equation x^3 = -343 is x = -7.
To solve the equation x^3 = -343, we need to find the value of x that satisfies this equation.
The given equation x^3 = -343 can be rewritten as x^3 + 343 = 0.
To find the solutions, we can use the fact that -343 is a perfect cube. It is equal to (-7)^3.
So, x^3 + 343 = 0 can be written as x^3 + (-7)^3 = 0.
Now we have the sum of two cubes, which can be factored as (x + 7)(x^2 - 7x + 49) = 0.
To find the values of x, we can set each factor equal to zero and solve for x:
x + 7 = 0, which gives x = -7.
x^2 - 7x + 49 = 0 is a quadratic equation. We can solve it using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a,
where a = 1, b = -7, and c = 49.
Plugging in these values, we get:
x = (-(-7) ± √((-7)^2 - 4(1)(49))) / (2(1))
= (7 ± √(49 - 196)) / 2
= (7 ± √(-147)) / 2.
Since the square root of a negative number is not a real number, there are no real solutions for x when taking the square root of -147.
Therefore, the only solution to x^3 = -343 is x = -7.