Grant was asked to solve 49x2−225=0
by factoring using the difference of squares pattern. What is/are the correct solution(s)?(1 point)
Responses
x=−157
, x=157
x equals negative Start Fraction 15 over 7 End Fraction , x equals Start Fraction 15 over 7 End Fraction
x=−715
, x=715
x equals negative Start Fraction 7 over 15 End Fraction , x equals Start Fraction 7 over 15 End Fraction
x=22549
, x=−22549
x equals Start Fraction 225 over 49 End Fraction , x equals negative Start Fraction 225 over 49 End Fraction
x=−157
, x=157
that is not a choice for a answer
Apologies for the confusion. In this case, the correct solutions would be x = -15/7 and x = 15/7.
To solve the equation 49x^2 - 225 = 0 using the difference of squares pattern, we can rewrite it as follows:
(7x)^2 - 15^2 = 0.
We can then factor it using the difference of squares pattern:
(7x + 15)(7x - 15) = 0.
To find the solutions, we set each factor equal to zero and solve for x:
7x + 15 = 0 --> 7x = -15 --> x = -15/7.
7x - 15 = 0 --> 7x = 15 --> x = 15/7.
Therefore, the correct solutions are:
x = -15/7,
x = 15/7.
So, the answer is "x equals negative 15/7, x equals 15/7."
To solve the equation 49x^2 - 225 = 0 using the difference of squares pattern, we need to factor it. The difference of squares pattern states that a^2 - b^2 can be factored into (a + b) (a - b). In this case, a^2 = 49x^2 and b^2 = 225.
To find the correct solution(s), we need to solve the equation (a + b) (a - b) = 0 for x.
In this equation, a^2 = (7x)^2 and b^2 = 15^2. So, we have (7x + 15) (7x - 15) = 0.
To find the values of x, we can set each factor equal to zero:
7x + 15 = 0, we subtract 15 from both sides to get 7x = -15. Then, we divide by 7 to solve for x, giving x = -15/7 or x = -2.143.
7x - 15 = 0, we add 15 to both sides to get 7x = 15. Then, we divide by 7 to solve for x, giving x = 15/7 or x = 2.143.
Therefore, the correct solutions are x = -15/7 or x = 15/7.
The answer given as x = -157, x = 157, x equals negative 15/7, and x equals 15/7 is incorrect.