Completing the square- Quad formula?

Question

Did I do this right? I got.... x+4=plus or minus the square root of 16.

x^2+8x-10=0

thanks if you can help me

Answer 1

No. The correct answer is x = -4 plus or minus the square root of 26

Completing the Square
When you start out trying to complete the square, the negative ten moves from the left side of the equation to the right side. When that -10 changes sides of the equation, it changes signs.

x^2 + 8x - 10 = 0
x^2 + 8x = 10
x^2 + 8x + 16 = 10 + 16 * How did I get 16
(x + 4)^2 = 26
square root of ((x+4)^2) = square root of 26
[the square root sign cancels the exponent of 2]
x+ 4 = plus or minus the square root of 26

solve for x

x = -4 plus or minus the square root of 26

*Take half of B (8 in this problem) and square it and add to both sides.

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The Quadratic Formula

x = [ -b +/- sq(b^2 - 4ac) ]/2a

Ax^2 + Bx + C = 0
1x^2 + 8x - 10 = 0

A = 1, B = 8, C = -10

x = [ -b +/- sq(b^2 - 4ac) ]/2a
x = [ -(8) +/- sq(8^2 - 4(1)(-10)) ]/2(1)
x = [ -8 +/- sq(64 + 40)]/2
x = [-8 +/- sq(104)]/2
x = [-8 +/- 2 * sq(26)]/2 [took square root of 104, 104 = 4 * 26]
4 is a perfect square so 2 comes
outside the radical sign adn 26 stays in
x = -4 +/- sq(26) [divided everything by 2]

x = -4 plus or minus the square root of 26

Answer 2

Completing the square: -
x² + 8x + 16 = 10 + 16
(x + 4)² = 26
x + 4 = ± √26
x = ±√26 - 4 = - 4 ±√26

Quadratic Formula: -
x = { - 8 ± √( 64 + 40) } / 2
x = { - 8 ± √104 } / 2
x = { - 8 ±√(4 x 26) } / 2
x = {- 8 ± 2√26 } / 2
x = - 4 ±√26

Answer 3

Close. You have to add something that will make the left-hand term a perfect square. In this case, to be a perfect square, you need to add 26 to both sides to get
x² + 8x + 16 = 26 and now the left side is
(x + 4)² = 26 so
x + 4 = ±√26 and
x = -4 ± √26

But you seem to have the general idea. Keep practicing!!! Math is like any other sport. The more you practice, the better you get ☺


Doug

Answer 4

Well...let's say you did. I'm not trying to be a pain, but rather help you understand a bit about your answer. If it was correct...why didn't you finish it? Think about the right side of the equasion...can it be simplified? If it can be, what does that give you as a value for x? Does it work out?

Ok, I'm hoping you've read the answer, looked at the problem and realized there's no way x could be 0 or -8. So what went wrong?

Remember, when you're done with a problem like this, you should be able to put your answer back into the equasion and have it work out correctly. It's the way you should check your work.

Answer 5

x^2+8x-10=0
x^2 + 8x = 10
x^2 + 8x +16 = 10 +16 =26
(x+4)^2 =26
x+4 = +/- sqrt(26)
x = -4 +/- sqrt(26)
Close, but off by 10.

Answer 6

if you complete the square, you'll get

y= x^2+8x-10
y= (x+4)^2 -26
if y =0

(x+4)^2 -26=0
x+4= plus minus root of 26

I think there must be a calculation mistake in your answer.

the formula is:
y=ax^2+bx+c where "a" must be equal to 1

y= (x+b/2)^2 -((b/2)^2)+c

You excluded the +c part

Answer 7

x^2 + 8 x - 10 = 0

x^2 + 2 (4x) + 16 - 16 - 10 = 0

(x + 4) ^2 - 26 = 0

(x + 4) ^2 - (sq. rt. 26) ^2 = 0

(x + 4 - sq. rt. 26) ( x + 4 + sq. rt. 26) = 0

x = sq. rt. 26 - 4 or x = 4 + sq rt. 26

Answer 8

-b plus minus square root (b^2 - 4ac), divide by 2a