To solve the equation 35 - x^2 + 2x = 0 by factoring, you can follow these steps:
Step 1: Write down the equation: 35 - x^2 + 2x = 0.
Step 2: Rearrange the equation to bring all terms on one side: x^2 - 2x - 35 = 0.
Step 3: Look for two numbers (let's call them a and b) whose sum is -2 (coefficient of x) and whose product is -35 (constant term).
Step 4: In this case, the numbers that satisfy these conditions are -7 and 5. Therefore, we can factor the equation as (x - 7)(x + 5) = 0.
Step 5: Set each factor equal to zero and solve for x individually:
- Setting (x - 7) = 0, we get x = 7.
- Setting (x + 5) = 0, we get x = -5.
Step 6: The solution set is the set of values that satisfy the equation, which in this case is {-5, 7}.
Step 7: To check if these solutions are correct, substitute them back into the original equation and see if they make it true. In this case, if you substitute x = -5 or x = 7 into the equation 35 - x^2 + 2x = 0, you will get 0 on both sides, confirming that these values are indeed solutions.