Question

Find the solutions of the quadratic equation x^2 + 4x - 21 = 0 by completing the square.

a) x = 3, x = -7
b) x = 5, x = -9
c) x = 2, x = -6
d) x = -5, x = 1

Answer 1

To solve the quadratic equation x^2 + 4x - 21 = 0 by completing the square, we first complete the square on the x terms and then solve for x, yielding the solutions x = 3 and x = -7.

Step-by-step explanation:

To find the solutions of the quadratic equation x^2 + 4x - 21 = 0 by completing the square, follow these steps:

Rewrite the equation grouping the x-terms together: x^2 + 4x = 21.

Add the square of half the coefficient of x to both sides to complete the square: (4/2)^2 = 4. So, x^2 + 4x + 4 = 21 + 4.

Simplify and write the left side as a square: (x + 2)^2 = 25.

Take the square root of both sides: x + 2 = ±5.

Solve for x: x = -2 ± 5, which gives us x = 3 and x = -7.

Therefore, the solutions of the quadratic equation are x = 3 and x = -7, which corresponds to option a).