2 Answers

Evans · Answer 1 · 2019-09-23T07:38:32+0000

We'll do this last last one real slow.

x^2 + 10 x + 25 = 8

Step one, move the 8 to the left side by subtracting it from 25:

x^2 + 10x + 17 = 0

To factor we'd need factors of 17 which add to 10. The only factors of 17 are 17 and 1 so there's no factoring. We use the quadratic formula.

$x= \frac 1 {2a}(-b \pm √(b^2-4ac))$

a, b and c refer to the coefficients on the quadratic equation. We have
x^2 + 10 x + 17 = 0 so a=1 (the coefficient on x^2) b=10, c=17.

$x= \frac 1 2(-10 \pm √(10^2-4(17)))$

Now we simplify the square root. 10²=100, 4(17)=68, so

$x = \frac 1 2(-10 \pm √(32))$

32 = 16(2) so we can simplify a bit more.

$x = \frac 1 2(-10 \pm 4 √(2))$

$x = -5 \pm 2 √(2)$

We compare to the answers and get

Answers: A E

With the Shakespeare Quadratic Formula shortcut

$x^2-2bx+c \textrm{ has zeros } x=b \pm √(b^2-c)$

Using that on
x^2 + 10x + 17 = 0 we could have gotten here a bit quicker. b=-5 this time, c=17, so

$x=-5 \pm √(25-17) = -5 \pm \sqrt 8 = -5 \pm 2 \sqrt 2$

Good luck. Please ask questions if you're still unsure.

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