How do you solve x^ { 2} - 11x + 19= - 5?

3 Answers
Dec 5, 2017

x = 3 , 8

Explanation:

STEP ONE: Add 5 to each side. You want all of the terms to be on one side before you start factoring!

x^2 -11x+19=-5

x^2 -11x+24=0

STEP TWO: Factor the equation! Two number that equal 24 when multiplied and -11 when added together are -8 and -3

x^2 -11x+24=0

(x-3)(x-8)

THEREFORE, x = 3 , 8

Dec 5, 2017

3=x=8

Explanation:

First, we turn the equation so that it equals zero.
x^2-11x+19=-5
x^2-11x+24=0

Let's see whether we could factor this.

We find the factors for 24:
1,24
2,12
3,8
4,6
-1,-24
-2,-12
-3,-8
-4,-6

We see that -3 and -8 add up to -11.

Therefore, x^2-11x+24=0 becomes (x-3)(x-8)=0
Therefore, our answers are 3 and 8.

You could have used the quadratic formula, but it is unnecessary in this case.

Dec 5, 2017

2 real solutions:

x=3\quad,\quad x=8

Explanation:

Rearrange the equation so it becomes a standard form quadratic equation, ax^2+bx+c.

x^2-11x+24, where:

  • a=1
  • b=-11
  • c=24

Plug those values into the quadratic formula:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

\implies x=\frac{11\pm\sqrt{(-11)^2-4(1)(24)}}{2(1)}

\implies x=\frac{11\pm\sqrt{121-96}}{2}

\implies x-\frac{11\pm5}{2}

\implies x=3\quad,\quad x=8