To solve the quadratic equation 2x^2 + 5x - 10 = 0, you can use the quadratic formula. The quadratic formula is:
x = (-b Ā± ā(b^2 - 4ac)) / (2a),
where a, b, and c are the coefficients of the equation.
In this case, a = 2, b = 5, and c = -10. Substituting these values into the quadratic formula, we get:
x = (-5 Ā± ā(5^2 - 4 * 2 * -10)) / (2 * 2).
Simplifying further, we have:
x = (-5 Ā± ā(25 + 80)) / 4,
x = (-5 Ā± ā105) / 4.
So the roots of the equation are:
x = (-5 + ā105) / 4 and x = (-5 - ā105) / 4.
These roots cannot be simplified any further, so your answers, x = (-5 + ā105) / 4 and x = (-5 - ā105) / 4, are correct and simplified as much as possible.