Solve by completing the square
x^2+4x-21=0
Help how do I do this???
For this go on to the website discovery education. Then go under students and click math. And then where it says step by step math in green, click on trigonmetry and calculus. I forgot what area of math this is but choose from one of the items. And jot it in the box search thing and when you press enter it gives you the answer with a wonderful explanation on how to get there. I've used it for math a couple of times.
x^2+4x-21=0
x^2+4x = 21
take half the middle term coefficient, square it, then add it to both sides
x^2 + 4x + 4 = 21 + 4
(x+2)^2 = 25
x+2 = ± √25 = ± 5
x = -2 ± 5
x = 3 or -7
To solve the quadratic equation x^2 + 4x - 21 = 0 by completing the square, follow these steps:
1. Make sure the equation is in standard form: ax^2 + bx + c = 0, where a, b, and c are constants.
In this example, the equation is already in standard form.
2. Take half of the coefficient of x (which is b) and square it. Add this value to both sides of the equation.
b = 4, so (4/2)^2 = 4 --> Add 4 to both sides:
x^2 + 4x - 21 + 4 = 0 + 4
The equation becomes: x^2 + 4x + 4 - 21 = 4
Simplify: x^2 + 4x - 17 = 4
3. Factor the perfect square trinomial on the left side of the equation.
The given equation can be written as: (x + 2)^2 - 17 = 4
4. Move the constant term to the right side of the equation.
(x + 2)^2 = 4 + 17
(x + 2)^2 = 21
5. Take the square root of both sides of the equation, considering both the positive and negative square roots.
x + 2 = √21 or x + 2 = -√21
6. Solve for x in each equation.
x + 2 = √21 --> x = -2 + √21
x + 2 = -√21 --> x = -2 - √21
So, the solutions to the quadratic equation x^2 + 4x - 21 = 0 are x = -2 + √21 and x = -2 - √21.