Question

Solve the equation: 𝑥squared + 11𝑥 − 26 = 0

Answer 1

To solve the equation 𝑥^2 + 11𝑥 − 26 = 0 using factoring, we need to find two numbers whose sum is 11 and whose product is -26. These numbers are 13 and -2.

Thus, the equation factors as (𝑥 + 13)(𝑥 - 2) = 0.

Setting each factor equal to zero gives 𝑥 + 13 = 0 or 𝑥 - 2 = 0.

Solving these equations:

For 𝑥 + 13 = 0, subtracting 13 from both sides gives 𝑥 = -13.

For 𝑥 - 2 = 0, adding 2 to both sides gives 𝑥 = 2.

Hence, the solutions to the equation 𝑥^2 + 11𝑥 − 26 = 0 are 𝑥 = -13 and 𝑥 = 2.