SOLUTION
Write out the quadratic equation
![x^2-14x+46=0](https://img.qammunity.org/2023/formulas/mathematics/college/70owerm4xdh8tf8yk0gym85nbxb2r588ak.png)
To solve by Completing the square, we apply the following steps
Step1: Take the constant term to the other side
![x^2-14x=-46](https://img.qammunity.org/2023/formulas/mathematics/high-school/767ukckbml4jbhy2di6mpaqq7rwjwfe9dw.png)
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}](https://img.qammunity.org/2023/formulas/mathematics/college/xcd8pzmkx4nmcz7f8733j19u948pahp15o.png)
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](https://img.qammunity.org/2023/formulas/mathematics/college/qyell5kyo4ayby3ht70blhqq14fzy2t5w6.png)
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}](https://img.qammunity.org/2023/formulas/mathematics/college/56qrlx0u3um8z5rxnvyflpmzcj09e0a1a4.png)
Step5: take the square root of both sides
![\begin{gathered} \sqrt[]{(x-7)^2}=\sqrt[]{3} \\ x-7=\pm\sqrt[]{3} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/p12zcik5rgjpbx2js1qon0pqud37o2q5bg.png)
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}](https://img.qammunity.org/2023/formulas/mathematics/college/9xootxyh7034gbmmi9gkgsct1f1345as4m.png)