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Topic: **Problem solving with quadratic equations****Question:**
i am used to solving quadratic equation with the quadratic formula, but i had a little problem with these quadratic equation.
here:
x^2 -25=0
here is another one
x^2 + 8x=0
my problem is.... do i have to use the formula to work this out??
Explain....In simplest way...Thanks!
x^2 is x square

May 21, 2019 / By Hannah

Question 1 x ² = 25 x = ± 5 Question 2 x = [ - 8 ± √64 ] / 2 x = [ - 8 ± 8 ] / 2 x = 0 , x = - 8 OR x (x + 8) = 0 x = 0 , x = - 8

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Did you like the answer? We found more questions related to the topic: **Problem solving with quadratic equations**

25. Don't get that problem since there are two variables. 32. Convert into standard form: 3x² + 8x + 2 = 0 Let: a = 3 b = 8 c = 2 So by quadratic formula: x = (-b ± √(b² - 4ac))/2a ⇒ (-8 ± √(8² - 4*3*2))/(2*3) ⇒ (-8 ± √(64 - 24))/6 ⇒ (-8 ± √40)/6 ⇒ (-8 ± √(4*10))/6 ⇒ (-8 ± 2√10)/6 ⇒ (-4 ± √10)/3 Let's see if you can solve the last problem by yourself.

These can both still be solved with the quadratic formula x² - 25 = 0 is equivalent to x² + 0x - 25 = 0 (b = 0) x² + 8x = 0 is equivalent to x² + 8x + 0 = 0 (c = 0) Of course, a simpler way would be to factorise them x² - 25 = 0 (x + 5)(x - 5) = 0 x + 5 = 0 or x - 5 = 0 x = ±5 x² + 8x = 0 x(x + 8) = 0 x = 0 or x + 8 = 0 x = {0, -8}

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The quadratic formula will work, of course, but both of these can be handled much more easily. Firstly, x^2-25 factors into (x-5)(x+5), so the roots are + and -5. Secondly, x^2 + 8x factors into x(x+8), so the roots are 0 and -8.

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The first example is a difference of two squares. You need to be able to spot these. If you are presented with something like a^2 - b^2 it will always factorise into (a+b)(a-b). a^2 - b^2 = (a+b)(a-b) - learn it. The second, you can start by taking the x out equation, so x^2 + 8x = 0 => x(x+8) = 0... (*) Remember, you cannot divide by x - since x could be zero. From (*) you can then say, since the two factors (x and x+8) mutliply to give zero, one of them must be zero for the equation to be satisfied. so x=0, or x+8=0 => x=-8. Hope that was simple enough!

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x^2 -- 25 = 0 => x^2 = 25 => x^2 = 5^2 => x = sqrt(5^2) = 5, --5 x^2 + 8x = 0 => x(x + 8) = 0 giving x = 0 or x + 8 = 0 => x = --8

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Just to be sure: the question is to solve x^2 - sqrt(7x) + 2 = 0 ? If so, I don't think there's an analytical solution for this form - so it's a numerical job - and this particular one doesn't have any solutions. PS "Its a complex number solution" Ah, I didn't know whether you were at a level where these were allowed. x^2 - sqrt(7x) + 2 only has a mininum in reals.

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