can show me how to solve this one?x2 + 4x - 21 = 0
(x+7)(x-3)
To solve the quadratic equation x^2 + 4x - 21 = 0, you can use the factoring method. Here are the steps to solve it:
Step 1: Identify the coefficients of the quadratic equation. In this case, the coefficient of x^2 is 1, the coefficient of x is 4, and the constant term is -21.
Step 2: Look for two numbers that multiply to give the constant term (-21) and add up to give the coefficient of x (4). In this case, the numbers are 7 and -3 since 7 * -3 = -21 and 7 + (-3) = 4.
Step 3: Rewrite the quadratic equation using these numbers as the coefficients of the x terms. So the equation becomes:
(x + 7)(x - 3) = 0
Step 4: Set each factor equal to zero. So you can set (x + 7) = 0 or (x - 3) = 0.
Step 5: Solve for x. For (x + 7) = 0, subtract 7 from both sides to get x = -7. For (x - 3) = 0, add 3 to both sides to get x = 3.
Therefore, the solutions to the quadratic equation x^2 + 4x - 21 = 0 are x = -7 and x = 3.