Completing the square

Question

x^2+2x-19 solve Quadratic Equation by completing the square.

Answer 1

I'm going to do this one step-by-step.

Setting the quadratic equal to zero, now we can proceed as normal.

x² + 2x - 19 = 0

In the case of completing the square, we will perform an inverse operation on term c by adding 19 to both sides to get our equation in the form ax² + bx = c

x² + 2x - 19 + (19) = 0 + (19)

x² + 2x = 19

Now we're ready to perform the following operations:

Take the coefficient b, divide it in half, and add the quotient to both sides:

Think of it as this: ax² + bx + (b/2) = c + (b/2)

x² + 2x + (2/2) = 19 + (2/2)

x² + 2x + (1) = 19 + (1)

x² + 2x + 1 = 20

Now, we must get the trinomial into a binomial form:

(x + 1)² = 20

To undo exponentiation, we'll square root both sides,

sqrt [ (x+1)² ] = sqrt [ 20 ]

x + 1 = ± sqrt(20)

x + 1 - (1) = ± sqrt(20) - (1)

We simplify the radical expression by pulling a 4 out of the radicand, 20:

sqrt([4] * 5)

2 sqrt(5)

And here, we have our two solutions:

x = -1 + 2 sqrt(5)

x = -1 - 2 sqrt(5)

Answer 2

x^2 +2x -19 = 0

x^2 + 2x = 19

x^2 +2x + 1 = 19 +1

(x+1)^2 = 20

x+1 = + or - sqr(20)

x = -1 + or - 2sqr5

x = -1 + 2sqr5 (that's the exact answer that you probably want)

but you can find an approximate rational answer as well

x = about -1 +2(2.24) or -1 - 2(2.24)

x = about 3.5 or -5.5

x = -5.5, 3.5

or

x= -5.472, 3.472 rounded to 3 decimal places

x^2 +2x -19 = 0

(3.472)^2 + 2(3.472) -19 =0

18.999 -19 = -.001

x^2+2x -19 = 0

using the quadratic formula

x= -2/2 + or -(1/2)sqr(4+4(19)

= -1 + or - (1/2)4sqr5

=-1 + or - 2sqr5

=-1 + or -4.472

=-5.472, 3.472