Question

Sole the quadratic equation by completing the square. x^2-14x+46=0Choose the appropriate form and fill in the blanks with the correct numbers. Then solve the equation. If there’s more than one solution, separate them with commas.

Answer 1

Write out the quadratic equation

`x^2-14x+46=0`

To solve by Completing the square, we apply the following steps

Step1: Take the constant term to the other side

`x^2-14x=-46`

Step2: Get half of the coefficient of x

`\begin{gathered} Co-\text{efficient of x =14} \\ \text{ Half of the co}efficient\text{ of x=}\frac{\text{14}}{2}=7 \end{gathered}`

Step3: Square the result in step 2 and add it to the equation in the equation in step1

`x^2-14x+7^2=-46+7^2`

Step4: Factorize the left-hand side and simplify the right-hand side of the equation in step 3

`\begin{gathered} (x-7)^2=-46+49 \\ (x-7)^2=3 \end{gathered}`

Step5: take the square root of both sides

`\begin{gathered} \sqrt[]{(x-7)^2}=\sqrt[]{3} \\ x-7=\pm\sqrt[]{3} \end{gathered}`

Hence the value of x is

`\begin{gathered} x=7\pm\sqrt[]{3} \\ \text{Then the two values of x are } \\ x=(7+\sqrt[]{3}),(7-\sqrt[]{3})_{} \end{gathered}`