Change 2x^2-5x=25 to standard form. Then find the solution set.
To change the given equation into standard form, we need to set it equal to zero. So, let's rearrange the equation.
2x^2 - 5x = 25
First, subtract 25 from both sides of the equation.
2x^2 - 5x - 25 = 0
Now, the equation is in standard form.
To find the solution set, we can use factoring, completing the square, or the quadratic formula. In this case, let's use factoring.
The equation we have is a quadratic equation. We need to find two numbers whose product is the coefficient of x^2 (which is 2) and whose sum is the coefficient of x (which is -5).
The numbers that multiply to give 2 are 2 and 1, and the numbers whose sum is -5 are -2 and -3.
Therefore, we can rewrite the equation as:
(2x + 3)(x - 5) = 0
Now, set each factor equal to zero and solve for x.
2x + 3 = 0 or x - 5 = 0
For the first equation, subtract 3 from both sides:
2x = -3
Divide both sides by 2:
x = -3/2
For the second equation, add 5 to both sides:
x = 5
So, the solution set for the given equation is { x = -3/2, x = 5 }.