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Consider the equation: x2 – 3x = 18A) First, use the "completing the square" process to write this equation in the form (x + D)² =or (2 – D)? = E. Enter the values of D and E as reduced fractions or integers.=z? - 3x = 18 is equivalent to:– 3rPreview left side of egn:B) Solve your equation and enter your answers below as a list of numbers, separated with a commawhere necessary.Answer(s):

Consider The Equation X2 3x 18A First Use The Completing The Square Process To Write This Equation In The Form X D Or 2 D E Enter The Values Of D And E As Reduc class=

Sagot :

Part A.

The quadratic equation,

[tex]ax^2+bx+c=0[/tex]

is equivalent to

[tex]a(x+\frac{b}{2a})^2=\frac{b^2}{4a}-c[/tex]

In our case a=1, b=-3 and c=-18. Then, by substituting these value into the last result, we have

[tex](x+\frac{-3}{2(1)})^2=(\frac{-3}{2(1)})^2+18[/tex]

which gives

[tex]\begin{gathered} (x-\frac{3}{2})^2=\frac{9}{4}+18 \\ (x-\frac{3}{2})^2=\frac{9}{4}+18 \\ (x-\frac{3}{2})^2=\frac{9+72}{4} \\ (x-\frac{3}{2})^2=\frac{81}{4} \end{gathered}[/tex]

Therefore, the answer for part A is:

[tex](x-\frac{3}{2})^2=\frac{81}{4}[/tex]

Part B.

Now, we need to solve the last result for x. Then, by applying square root to both sides, we have

[tex]x-\frac{3}{2}=\pm\sqrt[]{\frac{81}{4}}[/tex]

which gives

[tex]x-\frac{3}{2}=\pm\frac{9}{2}[/tex]

then, by adding 3/2 to both sides, we obtain

[tex]x=\frac{3}{2}\pm\frac{9}{2}[/tex]

Then, we have 2 solutions,

[tex]\begin{gathered} x=\frac{3}{2}+\frac{9}{2}=\frac{12}{2}=6 \\ \text{and} \\ x=\frac{3}{2}-\frac{9}{2}=\frac{-6}{2}=-3 \end{gathered}[/tex]

Therefore, the answer for part B is: -3, 6

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