Solve each equation by completing the square need help please

QUESTION POSTED AT 29/05/2020 - 01:23 AM

Answered by admin AT 29/05/2020 - 01:23 AM

Okay, first let's complete the square.

x^2 - 6x + 2 = 0
First, get the +2 to the other side of the equal sign by subtracting 2 from both sides.

x^2 - 6x + 2 = 0
               -2    -2
x^2 - 6x = -2.

Now we have to turn our first binomial (x^2 - 6x) into a perfect square trinomial. To do this, we simply divide the second term's coefficient by 2, and then square the result.

-6 / 2 = -3, -3^2 = 9.
We just add this to both sides of the equation.

x^2 - 6x = -2
x^2 - 6x + 9 = -2 + 9
x^2 - 6x + 9 = 7

Now, we need to factor our first trinomial.
Because our trinomial is a perfect square trinomial, we can put it in the form (a + b)^2. To do this, we just take the square root of the first term and the square root of the last term.

√x^2 = x, √9 = 3.

So, x^2 - 6x + 9 factored is (x + 3)^2.

Now we have (x + 3)^2 = 7, and we have finished completing the square.
Now we need to solve for the x intercepts.

Take the square root of both sides of the equal sign, so
√(x + 3)^2 = +/- √7
x + 3 = +/- √7. √7 rounded to the nearest tenth is 2.6.

x + 3 = +/- 2.6, subtract 3 from both sides.
    -3    -3
x = +/- 2.6 - 3

x = 2.6 - 3 = -0.4
x = -2.6 - 3 = -5.6

So our x intercepts our approximately -0.4 and -5.6.

Hope this helps!!
Let me know if there's anything you don't understand and I'll try to explain as best I can.
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