Question

Solve the quadratic equation by completing the square.First, choose the appropriate form and fill in the blanks with the correct numbers.Then, solve the equation. Round your answer to the nearest hundredth.If there is more than one solution, separate them with commas.

Answer 1

Solution

Given

$x^2+2x-2=0\text{ ----------\lparen1\rparen}$

Using the completing the square method

Adding 2 to both sides of equation 1.

$\begin{gathered} x^2+2x-2+2=2 \\ \\ \Rightarrow x^2+2x=2 \end{gathered}$

Adding square of half of the coefficient of x to both sides

$\begin{gathered} x^2+2x+(\frac{2}{2})^2=2+(\frac{2}{2})^2 \\ \\ \Rightarrow x^2+2x+1=2+1 \\ \\ \Rightarrow x^2+2x+1=3 \\ \\ \Rightarrow(x+1)^2=3 \end{gathered}$

Taking the square roots of both sides,

$\begin{gathered} x+1=\pm\sqrt{3} \\ \\ \Rightarrow x=-1\pm\sqrt{3} \end{gathered}$