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Solve 2 x x − =− 6 5 by completing the square.Show all work for the steps below.(a) For 2 x xc c − + =− + 6 5 , what value of c is used to complete the square? (b) Substitute the value for c in Part 2(a). Then complete the square to rewrite the equation as the square of a binomial. (c) Solve for x.can you walk me through this one?

Solve 2 X X 6 5 By Completing The SquareShow All Work For The Steps Belowa For 2 X Xc C 6 5 What Value Of C Is Used To Complete The Square B Substitute The Valu class=

Sagot :

Part a. We are given the following quadratic equation:

[tex]x^2-6x=-5[/tex]

This is an equation of the form:

[tex]x^2+bx=c[/tex]

To complete the square we will add and subtract the following term:

[tex](\frac{b}{2})^2[/tex]

Substituting we get:

[tex](\frac{-6}{2})^2[/tex]

Solving the operations and simplifying we get:

[tex](\frac{-6}{2})^2=(-3)^2=9[/tex]

Therefore, the value of "c" is 9.

Part b. We will substitute the value of "c" in the equation:

[tex]x^2-6x+9=-5+9[/tex]

Now, we solve the operation on the right side:

[tex]x^2-6x+9=4[/tex]

Now, we will factor the left side using the square of a binomial. Therefore, we take the square root of the first and third term and rearrange them in the form of the square of a binomial, like this:

[tex](x-3)^2=4[/tex]

This completes part B.

Part C. Now, we will solve for "x". To do that we will take the square root to both sides:

[tex]\begin{gathered} x-3=\sqrt[]{4} \\ x-3=\pm2 \end{gathered}[/tex]

Now we add 3 to both sides:

[tex]x=3\pm2[/tex]

Since we have a quadratic equation there are two possible solutions for "x". The first solution is determined using the plus sign:

[tex]x=3+2=5[/tex]

The second solution is determined using the minus sign:

[tex]x=3-2=1[/tex]

Therefore, the values of "x" are 5 and 1.

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