Solve the quadratic by factoring.x, squared, minus, 38, equals, minus, 3, x, minus, 10x 2 −38=−3x−10

First, let's rewrite the equation in standard form, which is ax^2 + bx + c = 0.

So, the equation becomes: x^2 + 3x + 10x - 38 = 0

Combine like terms: x^2 + 13x - 38 = 0

Now, we need to factor the quadratic equation. We're looking for two numbers that multiply to -38 (the c term) and add to 13 (the b term).

Those numbers are -2 and 19, because -2*19 = -38 and -2 + 19 = 13.

So, we can rewrite the equation as: (x - 2)(x + 19) = 0

Setting each factor equal to zero gives the solutions to the equation:

x - 2 = 0 => x = 2

x + 19 = 0 => x = -19

So, the solutions to the equation x^2 + 13x - 38 = 0 are x = 2 and x = -19.