solve this equation by completing the square.
x^2+4x-21=0
halve the middle term, then square it, then balance the equation by adding it to one end of the = side and subtracting it from the other. Then get everything over to the left side so you have 0 left again on the right side, simplify, and factor. After factoring, take the two bubbles and set each equal to zero. This is how you get two numbers. Check your answers to make sure both of them work, because sometimes only one works.
To solve the equation x^2 + 4x - 21 = 0 by completing the square, follow these steps:
Step 1: Move the constant term (-21) to the other side of the equation to isolate the variable terms.
x^2 + 4x = 21
Step 2: Take half of the coefficient of x (4) and square it. Add this value to both sides of the equation.
x^2 + 4x + (4/2)^2 = 21 + (4/2)^2
x^2 + 4x + 4 = 21 + 4
Simplifying further:
x^2 + 4x + 4 = 25
Step 3: Rewrite the left side of the equation as a perfect square.
(x + 2)^2 = 25
Step 4: Take the square root of both sides of the equation while considering both positive and negative roots.
x + 2 = ±√25
Simplifying further:
x + 2 = ±5
Step 5: Solve for x by subtracting 2 from both sides of the equation.
x = -2 ± 5
This gives two possible solutions:
x = -2 + 5 = 3
x = -2 - 5 = -7
So, the equation x^2 + 4x - 21 = 0 is satisfied when x equals either 3 or -7.