Question

Please solve number 9. Solve each equation by completing the square. Simplify all irrational and complex solutions

Answer 1

Given

Solve using completing the square

$x^2-8x+4\text{ =0}$

Step 1

Keep x terms on the left and move the constant to the right side

by subtracting it on both sides

$x^2-8x=-4$

Step 2

Take half of the x term and square it

$(-8\text{ }\times\frac{1}{2})^2=16$

Step 3

Then add the result (16) to both sides

$x^2-8x+16=-4+16$

Step 4

Rewrite the perfect square on the left

$(x-4)^2=-4+16$

and combine terms on the right

$(x-4)^2=12$

Step 5

Take the square root of both sides

$x-4=\pm\sqrt[]{12}$

Simplify the Radical

$x-4=\pm2\sqrt[]{3}$

Step 6

Isolate the x on the left side and

solve for x

$x=4\pm2\sqrt[]{3}$

therefore

$\begin{gathered} x=4+2\sqrt[]{3} \\ \\ x=4-2\sqrt[]{3} \end{gathered}$

which becomes

x = 7.4641

x = 0.535898